Splitting scheme for the stability of strong shock profile

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:261

Article

Du, Linglong¹ 

[1] Donghua Univ, Dept Appl Math, Shanghai, Peoples R China

关键词: Splitting scheme;    Strong shock profile;    Dirichlet-Neumann map;    Conservation law;    Nonlinear stability;   

DOI  :  10.1016/j.jde.2016.06.018

来源: Elsevier

【 摘 要 】

In this paper, we use the Laplace transform and Dirichlet-Neumann map to give a systematical scheme to study the small wave perturbation of general shock profile with general amplitude. Here we use certain non-classical shock waves for a rotationally invariant system of viscous conservation laws to demonstrate this scheme. We derive an explicit solution and show that it converges pointwise to another over-compressive profile exponentially, when the perturbations of the initial data to a given over-compressive shock profile are sufficiently small. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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