Nonlinear asymptotic stability of non-self-similar rarefaction wave for two-dimensional viscous Burgers equation

2024/12/30 by Feimin Huang, Huang, Feimin, Guiqin Qiu +5
Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2412.20957

openalex publication_date 2024/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the large time behavior of solutions to the two-dimensional viscous Burgers equation u_t+uu_x+uu_y=Δu, toward a non-self-similar rarefaction wave of inviscid Burgers equation with two initial constant states, seperated by a curve y=φ(x), and prove that the above 2D non-self-similar rarefaction wave is time-asymptotically stable. Furthermore, we also get the decay rate. Both the rarefaction wave strength and the initial perturbation can be large.

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