Mats Ehrnstrom
About
Nonlinear and nonlocal dispersive partial differential equations
- Existence and properties of steady water waves with vorticity and critical layers
- Nonlocal model equations of very weak dispersion (Whitham type): global branches of solutions, highest waves and regularity
- Solitary and periodic waves in dispersive model equations and systems
- Enhanced existence time and questions related to blow-up
- Data-driven PDEs in connection to water waves and neuroscience
Current research group
Kristoffer Varholm (Postdoc), Douglas Svensson Seth (Postdoc), Fredrik Hildrum (Postdoc), Swati Yadav (Postdoc), Jun Xue (PhD), Johanna Ulvedal Marstrander (PhD).
Former members (PhDs and Postdocs): Yuya Suzuki, Mathias Nikolai Arnesen, Hung Le, Long Pei, Ola Isaac Høgåsen Mæhlen, Yuexun Wang, Dag Nilsson, Gabriele Brüll, Raj Dhara, Filippo Remonato
Active projects and programmes
- Leader of the RCN Large-scale interdisciplinary researcher project IMod. Partial differential equations, statistics and data: An interdisciplinary approach to data-based modelling, 2022–2028.
I am a member of the The Royal Norwegian Society of Sciences and Letters. CV available for download above.
Preprints and online first
- M. N. Arnesen, M. Ehrnstrom and A. G. Stefanov. A maximisation technique for solitary waves: the case of the nonlocally dispersive Whitham equation. 41 pages. arxiv:2303.14036
- M. Ehrnström, O. I. H. Mæhlen and K. Varholm. On the precise cusped behaviour of extreme solutions to Whitham-type equations. 30 pages. arxiv:2302.08856
Publications
2025
-
Mæhlen, Ola Isaac Høgåsen;
Varholm, Kristoffer;
Ehrnstrom, Mats.
(2025)
On the precise cusped behaviour of extreme solutions to Whitham-type equations.
Annales de l'Institut Henri Poincare. Analyse non linéar
Academic article
2024
-
Arnesen, Mathias Nikolai;
Ehrnstrom, Mats;
Stefanov, Atanas G..
(2024)
A Maximisation Technique for Solitary Waves: The Case of the Nonlocally Dispersive Whitham Equation.
Archive for Rational Mechanics and Analysis
Academic article
2023
-
Ehrnstrom, Mats;
Walsh, Samuel;
Zeng, Chongchun.
(2023)
Smooth stationary water waves with exponentially localized vorticity.
Journal of the European Mathematical Society (Print)
Academic article
2022
-
Ehrnstrom, Mats;
Nik, Katerina;
Walker, Christoph.
(2022)
A direct construction of a full family of Whitham solitary waves.
Proceedings of the American Mathematical Society
Academic article
-
Ehrnstrom, Mats;
Nilsson, Dag;
Groves, Mark D.
(2022)
Existence of Davey–Stewartson type solitary waves for the fully dispersive Kadomtsev–Petviashvilii equation.
SIAM Journal on Mathematical Analysis
Academic article
-
Ehrnstrom, Mats;
Wang, Yuexun.
(2022)
Enhanced existence time of solutions to evolution equations of Whitham type.
Discrete and Continuous Dynamical Systems. Series A
Academic article
2019
-
Ehrnstrom, Mats;
Wahlén, Erik.
(2019)
On Whitham's conjecture of a highest cusped wave for a nonlocal dispersive equation.
Annales de l'Institut Henri Poincare. Analyse non linéar
Academic article
-
Ehrnstrom, Mats;
Wang, Yuexun.
(2019)
Enhanced existence time of solutions to the fractional Korteweg de Vries equation.
SIAM Journal on Mathematical Analysis
Academic article
-
Ehrnstrom, Mats;
Remonato, Filippo;
Mæhlen, Ola Isaac Høgåsen;
Johnson, Mathew A.
(2019)
On the Bifurcation Diagram of the Capillary–Gravity Whitham Equation.
Water Waves
Academic article
2018
-
Ehrnstrom, Mats;
Pei, Long.
(2018)
Classical well-posedness in dispersive equations with nonlinearities of mild regularity, and a composition theorem in Besov spaces.
Journal of evolution equations (Printed ed.)
Academic article
-
Ehrnstrom, Mats;
Groves, Mark D.
(2018)
Small-amplitude fully localised solitary waves for the full-dispersion Kadomtsev-Petviashvili equation.
Nonlinearity
Academic article
-
Ehrnstrom, Mats;
Johnson, Mathew A;
Claassen, Kyle M.
(2018)
Existence of a Highest Wave in a Fully Dispersive Two-Way Shallow Water Model.
Archive for Rational Mechanics and Analysis
Academic article
2017
-
Brüll, Gabriele;
Ehrnstrom, Mats;
Pei, Long.
(2017)
Symmetry and decay of traveling wave solutions to the Whitham equation.
Journal of Differential Equations
Academic article
-
Bruell, Gabriele;
Ehrnstrom, Mats;
Geyer, Anna;
Pei, Long.
(2017)
Symmetric solutions of evolutionary partial differential equations.
Nonlinearity
Academic article
2015
-
Ehrnstrom, Mats.
(2015)
On Whitham's conjecture of a highest cusped wave for a nonlocal shallow water wave equation.
Oberwolfach Reports
Academic article
-
Ehrnstrom, Mats;
Escher, Joachim;
Pei, Long.
(2015)
A note on the local well-posedness for the whitham equation.
Springer Proceedings in Mathematics
Academic article
2014
-
Ehrnström, Mats Harald Andreas;
Wahlén, E..
(2014)
Trimodal Steady Water Waves.
Archive for Rational Mechanics and Analysis
Academic article
2013
-
Ehrnström, Mats Harald Andreas;
Kalisch, Henrik.
(2013)
Global bifurcation for the Whitham equation.
Mathematical Modelling of Natural Phenomena
Academic article
-
Ehrnström, Mats Harald Andreas;
Escher, Joachim;
Matioc, Bogdan-Vasile.
(2013)
Steady-state fingering patterns for a periodic Muskat problem.
Methods and Applications of Analysis
Academic article
2012
-
Ehrnström, Mats Harald Andreas;
Groves, Mark;
Wahlén, E..
(2012)
On the existence and stability of solitary-wave solutions to a class of evolution equations of Whitham type.
Nonlinearity
Academic article
2011
-
Ehrnström, Mats;
Escher, J.;
Villari, G..
(2011)
Steady water waves with multiple critical layers: interior dynamics.
Journal of Mathematical Fluid Mechanics
Academic article
-
Ehrnström, Mats;
Escher, J.;
Matioc, B.-V..
(2011)
Well-posedness, instabilities, and bifurcation results for the flow in a rotating Hele-Shaw cell.
Journal of Mathematical Fluid Mechanics
Academic article
-
Ehrnström, Mats;
Tisdell, C.C.;
Wahlén, E..
(2011)
Asymptotic integration of second order nonlinear difference equations.
Glasgow Mathematical Journal
Academic article
-
Ehrnström, Mats;
Escher, J.;
Wahlén, E..
(2011)
Steady water waves with multiple critical layers.
SIAM Journal on Mathematical Analysis
Academic article
Journal publications
-
Mæhlen, Ola Isaac Høgåsen;
Varholm, Kristoffer;
Ehrnstrom, Mats.
(2025)
On the precise cusped behaviour of extreme solutions to Whitham-type equations.
Annales de l'Institut Henri Poincare. Analyse non linéar
Academic article
-
Arnesen, Mathias Nikolai;
Ehrnstrom, Mats;
Stefanov, Atanas G..
(2024)
A Maximisation Technique for Solitary Waves: The Case of the Nonlocally Dispersive Whitham Equation.
Archive for Rational Mechanics and Analysis
Academic article
-
Ehrnstrom, Mats;
Walsh, Samuel;
Zeng, Chongchun.
(2023)
Smooth stationary water waves with exponentially localized vorticity.
Journal of the European Mathematical Society (Print)
Academic article
-
Ehrnstrom, Mats;
Nik, Katerina;
Walker, Christoph.
(2022)
A direct construction of a full family of Whitham solitary waves.
Proceedings of the American Mathematical Society
Academic article
-
Ehrnstrom, Mats;
Nilsson, Dag;
Groves, Mark D.
(2022)
Existence of Davey–Stewartson type solitary waves for the fully dispersive Kadomtsev–Petviashvilii equation.
SIAM Journal on Mathematical Analysis
Academic article
-
Ehrnstrom, Mats;
Wang, Yuexun.
(2022)
Enhanced existence time of solutions to evolution equations of Whitham type.
Discrete and Continuous Dynamical Systems. Series A
Academic article
-
Ehrnstrom, Mats;
Wahlén, Erik.
(2019)
On Whitham's conjecture of a highest cusped wave for a nonlocal dispersive equation.
Annales de l'Institut Henri Poincare. Analyse non linéar
Academic article
-
Ehrnstrom, Mats;
Wang, Yuexun.
(2019)
Enhanced existence time of solutions to the fractional Korteweg de Vries equation.
SIAM Journal on Mathematical Analysis
Academic article
-
Ehrnstrom, Mats;
Remonato, Filippo;
Mæhlen, Ola Isaac Høgåsen;
Johnson, Mathew A.
(2019)
On the Bifurcation Diagram of the Capillary–Gravity Whitham Equation.
Water Waves
Academic article
-
Ehrnstrom, Mats;
Pei, Long.
(2018)
Classical well-posedness in dispersive equations with nonlinearities of mild regularity, and a composition theorem in Besov spaces.
Journal of evolution equations (Printed ed.)
Academic article
-
Ehrnstrom, Mats;
Groves, Mark D.
(2018)
Small-amplitude fully localised solitary waves for the full-dispersion Kadomtsev-Petviashvili equation.
Nonlinearity
Academic article
-
Ehrnstrom, Mats;
Johnson, Mathew A;
Claassen, Kyle M.
(2018)
Existence of a Highest Wave in a Fully Dispersive Two-Way Shallow Water Model.
Archive for Rational Mechanics and Analysis
Academic article
-
Brüll, Gabriele;
Ehrnstrom, Mats;
Pei, Long.
(2017)
Symmetry and decay of traveling wave solutions to the Whitham equation.
Journal of Differential Equations
Academic article
-
Bruell, Gabriele;
Ehrnstrom, Mats;
Geyer, Anna;
Pei, Long.
(2017)
Symmetric solutions of evolutionary partial differential equations.
Nonlinearity
Academic article
-
Ehrnstrom, Mats.
(2015)
On Whitham's conjecture of a highest cusped wave for a nonlocal shallow water wave equation.
Oberwolfach Reports
Academic article
-
Ehrnstrom, Mats;
Escher, Joachim;
Pei, Long.
(2015)
A note on the local well-posedness for the whitham equation.
Springer Proceedings in Mathematics
Academic article
-
Ehrnström, Mats Harald Andreas;
Wahlén, E..
(2014)
Trimodal Steady Water Waves.
Archive for Rational Mechanics and Analysis
Academic article
-
Ehrnström, Mats Harald Andreas;
Kalisch, Henrik.
(2013)
Global bifurcation for the Whitham equation.
Mathematical Modelling of Natural Phenomena
Academic article
-
Ehrnström, Mats Harald Andreas;
Escher, Joachim;
Matioc, Bogdan-Vasile.
(2013)
Steady-state fingering patterns for a periodic Muskat problem.
Methods and Applications of Analysis
Academic article
-
Ehrnström, Mats Harald Andreas;
Groves, Mark;
Wahlén, E..
(2012)
On the existence and stability of solitary-wave solutions to a class of evolution equations of Whitham type.
Nonlinearity
Academic article
-
Ehrnström, Mats;
Escher, J.;
Villari, G..
(2011)
Steady water waves with multiple critical layers: interior dynamics.
Journal of Mathematical Fluid Mechanics
Academic article
-
Ehrnström, Mats;
Escher, J.;
Matioc, B.-V..
(2011)
Well-posedness, instabilities, and bifurcation results for the flow in a rotating Hele-Shaw cell.
Journal of Mathematical Fluid Mechanics
Academic article
-
Ehrnström, Mats;
Tisdell, C.C.;
Wahlén, E..
(2011)
Asymptotic integration of second order nonlinear difference equations.
Glasgow Mathematical Journal
Academic article
-
Ehrnström, Mats;
Escher, J.;
Wahlén, E..
(2011)
Steady water waves with multiple critical layers.
SIAM Journal on Mathematical Analysis
Academic article
Outreach
2024
-
Academic lectureEhrnstrom, Mats. (2024) Asymmetric capillary–gravity water waves in the steady periodic setting. Lund University Mathematical Theory of Water Waves, Lund University 2024-08-20 - 2024-08-22
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Academic lectureEhrnstrom, Mats. (2024) Asymmetric capillary–gravity water waves in the steady periodic setting. Karlstad Universitet Mini-symposium on Water waves and free boundary problems in fluid mechanics. Equadiff 2024 2024-06-10 - 2024-06-14
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Academic lectureEhrnstrom, Mats. (2024) On two new constructions of solitary waves: The nonlinear and nonlocally dispersive Whitham equation. Bergen–Lund–Trondheim Workshop on Dispersive and Water Waves Equations , Bergen 2024-04-27 - 2024-04-28
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Academic lectureEhrnstrom, Mats. (2024) On two new constructions of solitary waves: The nonlinear and nonlocally dispersive Whitham equation. Université Paris–Saclay Seminar on Analysis and PDEs 2024-05-23 - 2024-05-23
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Academic lectureEhrnstrom, Mats. (2024) On two new constructions of solitary waves: The nonlinear and nonlocally dispersive Whitham equation. Martin-Luther-Universität Halle–Wittenberg Oberseminar Analysis 2024-05-21 - 2024-05-21
2023
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Popular scientific lectureEhrnstrom, Mats. (2023) On Euler’s musical function and other topics in the mathematical theory of music. Mathematical Pearls , NTNU 2023-10-20 -
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Academic lectureEhrnstrom, Mats. (2023) On two new constructions of solitary waves: the nonlinear and nonlocally dispersive Whitham equation. Aspects of Nonlinear Evolution. Conference in Honor of the 60th Birthday of Joachim Escher , Leibniz Universität Hannover 2023-05-31 - 2023-06-02
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Academic lectureEhrnstrom, Mats. (2023) On two new constructions of solitary waves: the nonlinear and nonlocally dispersive Whitham equation. Workshop on Nonlinear Waves and Related Topics, Kanagawa , Shonan Village Center 2023-11-06 - 2023-11-10
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Academic lectureEhrnstrom, Mats. (2023) Equations with very low order of dispersion. An overview and description of new results. Order and Randomness in Partial Differential Equations Water Waves and Integrable Systems. Workshop at Institut Mittag-Leffler. Dedicated to the memory of Thomas Kappeler , Institut Mittag–Leffler, Stockholm 2023-09-11 - 2023-09-15
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Academic lectureEhrnstrom, Mats. (2023) On two new constructions of solitary waves: the nonlinear and nonlocally dispersive Whitham equation. Seminar of Analysis, EPFL , École polytechnique fédérale de Lausanne 2023-03-17 -
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Popular scientific lectureEhrnstrom, Mats. (2023) Top-down and bottom-up: how the measure-prone can meet the principle-driven. IE Friday Talk , NTNU 2023-09-29 -
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Academic lectureEhrnstrom, Mats. (2023) Mathematics in Water Waves. Colloquium at Linköping University , Linköping University 2023-09-06 -
2022
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Academic lectureEhrnstrom, Mats. (2022) Existence of Davey–Stewartson type solitary waves for the fully dispersive Kadomtsev–Petviashvili equation. 2nd Norwegian meeting on PDEs , Bergen 2022-06-08 - 2022-06-10
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Academic lectureEhrnstrom, Mats. (2022) On some water wave solutions that have emanated from work with G. Villari. Two Days on Qualitative Theory of Differential Equations A conference in honor of Gabriele Villari , Università degli Studi di Firenze 2022-09-30 - 2022-10-01
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Academic lectureEhrnstrom, Mats. (2022) Smooth stationary water waves with exponentially localised vorticity. Program on Geometric Aspects of Nonlinear Partial Differential Equations , Institut Mittag-Leffler, Stockholm 2022-11-15 -
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Academic lectureEhrnstrom, Mats. (2022) Existence of Davey–Stewartson type solitary waves for the fully dispersive Kadomtsev–Petviashvili equation. Numerical and analytical approaches for nonlinear dispersive PDEs, Dijon , University of Burgundy 2022-06-13 - 2022-06-17
2021
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Academic lectureEhrnstrom, Mats. (2021) Smooth stationary water waves with exponentially localised vorticity. Mathematics of Fluid Dynamics program , MSRI, Berkeley 2021-04-06 -
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Academic lectureEhrnstrom, Mats. (2021) Constructions and properties of mathematical solutions to water wave equations. Hausdorff Colloquium , University of Bonn 2021-06-09 -
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Academic lectureEhrnstrom, Mats. (2021) Smooth stationary water waves with exponentially localised vorticity. PDE seminar, Lanzhou , Lanzhou University 2021-05-28 -
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Popular scientific lectureEhrnstrom, Mats. (2021) The Hardy-Weinberg Principle and Evolutionary Genetics. Mathematical Pearls , NTNU 2021-12-03 -
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Academic lectureEhrnstrom, Mats. (2021) Smooth stationary water waves with exponentially localised vorticity. PDE seminar, University of Missouri , University of Missouri (online) 2021-04-15 -
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Academic lectureEhrnstrom, Mats. (2021) On the bifurcation diagram of the capillary-gravity Whitham equation. Online Seminar on Nonlinear Water Waves and Related Topics , Ibaraki University 2021-11-19 -
2018
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Academic lectureEhrnstrom, Mats. (2018) Enhanced existence time of solutions to the fractional Korteweg—de Vries equation. One-day seminar on Geometry, Analysis and PDEs , Bergen 2018-10-22 - 2018-10-22
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Academic lectureEhrnstrom, Mats. (2018) Travelling water waves with localised vorticity. NMF National meeting of mathematicians , Bergen 2018-09-14 - 2018-09-14
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Academic lectureEhrnstrom, Mats. (2018) Enhanced existence time of solutions to the fractional Korteweg—de Vries equation. The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications Dynamics of fluids and nonlinear waves , Taipei 2018-07-08 - 2018-07-08
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Academic lectureEhrnstrom, Mats. (2018) On waves of greatest height in fully dispersive nonlocal wave equations. PDE seminar , University of Warsaw 2018-03-22 - 2018-03-22
2017
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Academic lectureEhrnstrom, Mats. (2017) Small-amplitude solitary waves for the full dispersion Kadomtsev–Petviashvili equation. Numerical Analysis and PDE seminar, L'université Paris-Sud (Paris-XI) , Orsay, Paris 2017-05-11 - 2017-05-11
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Academic lectureEhrnstrom, Mats. (2017) Small-amplitude solitary waves for the full-dispersion Kadomtsev-Petviashvili equation. Nonlinear Dispersive Partial Differential Equations and Inverse Scattering, Fields Institute , Fields Institute, Toronto 2017-08-08 - 2017-08-12
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Academic lectureEhrnstrom, Mats. (2017) Small-amplitude solitary waves for the full-dispersion Kadomtsev-Petviashvili equation. Session on Nonlinear PDE, Catalan, Spanish, Swedish Math Meeting 2017 , Umeå 2017-06-13 - 2017-06-15
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Academic lectureEhrnstrom, Mats. (2017) On waves of greatest height in fully dispersive equations. PDE seminar, Lund University , Lund 2017-06-29 - 2017-06-29
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Academic lectureEhrnstrom, Mats. (2017) Existence of a highest wave in a fully dispersive two-way shallow water model. Tenth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory , Athens, Georgia 2017-03-28 - 2017-03-31
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Academic lectureEhrnstrom, Mats. (2017) Small-amplitude solitary waves for the full dispersion Kadomtsev–Petviashvili equation. ICERM Semester Program on "Singularities and Waves In Incompressible Fluids": Workshop on Water Waves , ICERM, Brown University, Providence 2017-04-24 - 2017-04-28
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Academic lectureEhrnstrom, Mats. (2017) On waves of greatest height in fully dispersive nonlocal wave equations. Oberseminar in Analysis und Physik , Leibniz Universität Hannover 2017-01-17 - 2017-01-17
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Academic lectureRemonato, Filippo; Ehrnstrom, Mats; Johnson, Mathew; Kalisch, Henrik. (2017) Two-Dimensional Bifurcation in the Whitham equation with surface tension. IMACS Conference , Athens 2017-03-30 -
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LectureBruell, Gabriele; Ehrnstrom, Mats; Pei, Long. (2017) On symmetry and decay of travelling solutions to a nonlocal dispersive equation. Nonlinear Evolution Equations/Wave Phenomena 2017-03-28 - 2017-03-31
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LectureBruell, Gabriele; Pei, Long; Ehrnstrom, Mats. (2017) Symmetry and decay of travelling wave solutions to the Whitham equation. Analysis and PDE Seminar, University of Lyon I 2017-03-21 - 2017-03-21
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LectureBruell, Gabriele; Pei, Long; Ehrnstrom, Mats. (2017) On symmetry and decay of travelling wave solutions to a nonlocal dispersive equation. Analysis Seminar, TU Delft 2017-05-04 - 2017-05-04
2016
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Academic lectureEhrnstrom, Mats. (2016) On waves of greatest height in fully dispersive nonlocal wave equations. Banff International Research Station (BIRS) Theoretical and Computational Aspects of Nonlinear Surface Waves , Banff 2016-10-31 - 2017-12-04
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Academic lectureEhrnstrom, Mats. (2016) On waves of greatest height in fully dispersive nonlocal wave equations. Workshop ”Recent progress on the qualitative properties of nonlinear dispersive equations and systems” (Wolfgang Pauli Institute) 2016-09-19 - 2016-09-23
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Academic lectureEhrnstrom, Mats. (2016) On waves of greatest height in fully dispersive nonlocal wave equations. Workshop on Interactions between Partial Differential Equations and Functional Inequalities (Institut Mittag-Leffler) , Stockholm 2016-09-12 - 2016-09-16
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Academic lectureEhrnstrom, Mats. (2016) Symmetry and decay properties of traveling wave solutions to the Whitham equation. Differential Equations Seminar , University of Missouri 2016-12-03 -
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Academic lectureEhrnstrom, Mats. (2016) A presentation of the mathematical theory for the highest wave of the Whitham equation in connection to the awarding of the Wallenberg prize 2016. Svenska Matematikersamfundets årsmöte 2016-06-17 -
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Academic lectureEhrnstrom, Mats. (2016) On Whitham's conjecture of a highest cusped wave for a nonlocal shallow water wave equation. Oberseminar Analysis und Physik , Leibniz Universität Hannover 2016-02-01 -
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Academic lectureRemonato, Filippo; Ehrnstrom, Mats; Johnson, Mathew; Kalisch, Henrik. (2016) Two-dimensional bifurcation in the Whitham Equation with surface tension. AIMS Conference 2016-07-05 -
2015
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Academic lectureEhrnstrom, Mats. (2015) On Whitham's conjecture of a highest cusped wave for a nonlocal shallow water wave equation. Online seminar on Applied Partial Differential Equations (University of Washington) 2015-10-15 -
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Popular scientific lectureEhrnstrom, Mats. (2015) Water Waves --- a mathematician's apology for dispersive equations. Matematiske perler, Institutt for matematiske fag 2015-10-16 -
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Academic lectureEhrnstrom, Mats. (2015) Multi-dimensional bifurcation of steady water waves with vorticity. SIAM Conference on Analysis of Partial Differential Equations 2015-12-06 - 2016-12-10
2014
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InterviewLein, Hilde Lea; Brøseth, Heidi; Ehrnström, Mats Harald Andreas; Krokan, Arne; Mikkelsen, Solveig. (2014) Prosjekt Innovativ undervisning: Gjennombrudd for omvendt undervisning. universitetsavisa.no universitetsavisa.no [Internet] 2014-01-10