ASYMPTOTIC STABILITY OF GLOBAL SOLUTIONS FOR A CLASS OF SEMILINEAR WAVE EQUATION

doi:10.1007/s10473-025-0617-5

Abstract

Abstract: This paper establishes the asymptotic stability of a composite wave for a damped wave equation with partially linearly degenerate flux. The global solution is shown to converge to a combination of a rarefaction wave and a viscous contact wave as time tends to infinity by employing the $L^2$ energy method and a refined wave interaction analysis. This is the first result on the asymptotics toward multiwave for the damped wave equation, and this asymptotic stability result does not rely on the small assumption of neither the initial perturbations nor the wave strength.

Key words: asymptotic stability, rarefaction wave, viscous contact wave, linearly degenerate flux, $L^2$ energy method

CLC Number:

35B35

Mutong HE, Feimin HUANG, Tianyi WANG. ASYMPTOTIC STABILITY OF GLOBAL SOLUTIONS FOR A CLASS OF SEMILINEAR WAVE EQUATION[J].Acta mathematica scientia,Series B, 2025, 45(6): 2685-2714.

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