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 - <p>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 &gt; 1, 1 &lt; α &lt; 2, 0 &lt; β &lt; 2, 0 &lt; γ &lt; 1. Nonexistence results and necessary conditions for global existence are established by means of the test function method. This results extend previous works.</p>