Asymptotic profiles for a class of perturbed Burgers equations in one space dimension. (English) Zbl 1402.35142
Summary: In this article we consider the Burgers equation with some class of perturbations in one space dimension. Using various energy functionals in appropriate weighted Sobolev spaces rewritten in the variables \(\frac{\xi}{\sqrt\tau}\) and \(\log\tau\), we prove that the large time behavior of solutions is given by the self-similar solutions of the associated Burgers equation.
MSC:
| 35K55 | Nonlinear parabolic equations |
| 35B20 | Perturbations in context of PDEs |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35C20 | Asymptotic expansions of solutions to PDEs |
| 35L05 | Wave equation |
| 35L60 | First-order nonlinear hyperbolic equations |
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