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arXiv · 2209.03079

Convergence rate toward shock wave under periodic perturbation for generalized Korteweg-de Vries-Burgers equation

Lin Chang
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Abstract

In this paper, a viscous shock wave under space-periodic perturbation of generalized Korteweg-de Vries-Burgers equation is investigated. It is shown that if the initial periodic perturbation around the viscous shock wave is small, then the solution time asymptotically tends to a viscous shock wave with a shift partially determined by the periodic oscillations. Moreover the exponential time decay rate toward the viscous shock wave is also obtained for some certain perturbations.

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Lin Chang. 2022-09-07. Convergence rate toward shock wave under periodic perturbation for generalized Korteweg-de Vries-Burgers equation. https://arxiv.org/abs/2209.03079

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