ASYMPTOTIC STABILITY OF VISCOUS SHOCKS IN THE MODULAR BURGERS EQUATION
| Autor: | Pascal Poullet, Uyen Le, Dmitry E. Pelinovsky |
|---|---|
| Přispěvatelé: | McMaster University [Hamilton, Ontario], Department of Mathematics and Statistics, McMaster University, Hamilton, Canada, Laboratoire de Mathématiques Informatique et Applications (LAMIA), Université des Antilles et de la Guyane (UAG), Poullet, Pascal |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
General Physics and Astronomy
FOS: Physical sciences Dynamical Systems (math.DS) Pattern Formation and Solitons (nlin.PS) Space (mathematics) System of linear equations 01 natural sciences 010305 fluids & plasmas Mathematics - Analysis of PDEs modular Burgers equation Exponential stability Stability theory 0103 physical sciences FOS: Mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] 0101 mathematics Mathematics - Dynamical Systems [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP] Mathematical Physics Mathematics traveling fronts asymptotic stability Applied Mathematics 010102 general mathematics Mathematical analysis Statistical and Nonlinear Physics Mathematical Physics (math-ph) [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA] Nonlinear Sciences - Pattern Formation and Solitons Exponential function Burgers' equation Nonlinear system Gravitational singularity [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] Analysis of PDEs (math.AP) |
| Zdroj: | Nonlinearity Nonlinearity, IOP Publishing, In press HAL |
| ISSN: | 0951-7715 1361-6544 |
| Popis: | Dynamics of viscous shocks is considered in the modular Burgers equation, where the time evolution becomes complicated due to singularities produced by the modular nonlinearity. We prove that the viscous shocks are asymptotically stable under odd and general perturbations. For the odd perturbations, the proof relies on the reduction of the modular Burgers equation to a linear diffusion equation on a half-line. For the general perturbations, the proof is developed by converting the time-evolution problem to a system of linear equations coupled with a nonlinear equation for the interface position. Exponential weights in space are imposed on the initial data of general perturbations in order to gain the asymptotic decay of perturbations in time. We give numerical illustrations of asymptotic stability of the viscous shocks under general perturbations. Comment: 35 pages; 2 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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