TY - JOUR T1 - Non-existence of Global Solutions for a Fractional Wave-diffusion Equations AU - Berbiche , Mohamed AU - Hakem , Ali JO - Journal of Partial Differential Equations VL - 1 SP - 1 EP - 20 PY - 2012 DA - 2012/03 SN - 25 DO - http://doi.org/10.4208/jpde.v25.n1.1 UR - https://global-sci.org/intro/article_detail/jpde/5171.html KW - Nonlinear wave-diffusion equation KW - fractional power derivative KW - critical exponent AB -
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.