Blow-up and lifespan estimate for wave equations with critical damping term of space-dependent type related to Glassey conjecture

2022/04/19 by Ahmad Z. Fino, Fino, Ahmad Z., Mohamed Ali Hamza +1
Mathematics · Engineering · #Advanced Mathematical Physics Problems #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2204.09156

Abstract

The main purpose of the present paper is to study the blow-up problem of the wave equation with space-dependent damping in the scale-invariant case and time derivative nonlinearity with small initial data. Under appropriate initial data which are compactly supported, by using a test function method and taking into account the effect of the damping term (\fracμ√(1+|x|²)u_t), we provide that in higher dimensions the blow-up region is given by p ∈ (1, p_G(N+μ)] where p_G(N) is the Glassey exponent. Furthermore, we shall establish a blow-up region, independent of μ given by p∈ (1, 1+(2)/(N)), for appropriate initial data in the energy space with noncompact support.

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