Year: 2012
Author: Mohamed Berbiche, Ali Hakem
Journal of Partial Differential Equations, Vol. 25 (2012), Iss. 1 : pp. 1–20
Abstract
We considered the Cauchy problem for the fractional wave-diffusion equation $$D^αu-Δ|u|^{m-1}u+(-Δ)^{β/2}D^γ|u|^{l-1}u=h(x,t)|u|^p+f(x,t)$$ with given initial data and where p > 1, 1 < α < 2, 0 < β < 2, 0 < γ < 1. Nonexistence results and necessary conditions for global existence are established by means of the test function method. This results extend previous works.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v25.n1.1
Journal of Partial Differential Equations, Vol. 25 (2012), Iss. 1 : pp. 1–20
Published online: 2012-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Nonlinear wave-diffusion equation