Non-existence of Global Solutions for a Fractional Wave-diffusion Equations

Non-existence of Global Solutions for a Fractional Wave-diffusion Equations

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

Author Details

Mohamed Berbiche

Ali Hakem