Blow-up of solutions to semilinear wave equations with a time-dependent strong damping

2021/11/02 by Ahmad Z. Fino, Fino, Ahmad Z., M. H. Hamza +1
Mathematics · Engineering · #Advanced Mathematical Physics Problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2111.01433

Abstract

The paper investigates a class of a semilinear wave equation with time-dependent damping term (-\frac1(1+t)^βΔu_t) and a nonlinearity |u|^p. We will show the influence of the the parameter β in the blow-up results under some hypothesis on the initial data and the exponent p by using the test function method. We also study the local existence in time of mild solution in the energy space H¹(ℝⁿ)× L²(ℝⁿ).

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