Global existence of solutions for semilinear damped wave equations with variable coefficients

2021/10/10 by Yuta Tamada, Tamada, Y.
Mathematics · Engineering · Physics and Astronomy · #Advanced Mathematical Physics Problems #Stability and Controllability of Differential Equations #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2110.04718

Abstract

We consider the Cauchy problem for the damped wave equations with variable coefficients a(x) having power type nonlinearity |u|^p. We discuss the global existence of solutions for small initial data and investigate the relation between the range of a(x) and the order p.

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