This is a summary of the papers [6], [7] done in collaboration with Tej-Eddine Ghoul and Nader Masmoudi and [2] done in collaboration with Nicola de Nitti. We are interested in the long time behavior of solutions of the viscous Burgers equation for a class of initial data with infinite mass. We show that, up to a rescaling, they converge to a limit profile that has a discontinuity. We investigate this profile and explain how to understand this discontinuity point.
@article{SLSEDP_2023-2024____A4_0, author = {Eliot Pacherie}, title = {Some asymptotic profiles for the viscous {Burgers} equation with infinite mass}, journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications}, note = {talk:16}, pages = {1--8}, publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique}, year = {2023-2024}, doi = {10.5802/slsedp.167}, language = {en}, url = {https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.167/} }
TY - JOUR AU - Eliot Pacherie TI - Some asymptotic profiles for the viscous Burgers equation with infinite mass JO - Séminaire Laurent Schwartz — EDP et applications N1 - talk:16 PY - 2023-2024 SP - 1 EP - 8 PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique UR - https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.167/ DO - 10.5802/slsedp.167 LA - en ID - SLSEDP_2023-2024____A4_0 ER -
%0 Journal Article %A Eliot Pacherie %T Some asymptotic profiles for the viscous Burgers equation with infinite mass %J Séminaire Laurent Schwartz — EDP et applications %Z talk:16 %D 2023-2024 %P 1-8 %I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique %U https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.167/ %R 10.5802/slsedp.167 %G en %F SLSEDP_2023-2024____A4_0
Eliot Pacherie. Some asymptotic profiles for the viscous Burgers equation with infinite mass. Séminaire Laurent Schwartz — EDP et applications (2023-2024), Exposé no. 16, 8 p. doi : 10.5802/slsedp.167. https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.167/
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