Mohamed Berbiche and Ali Hakem

Necessary and Sufficient Conditions for Nonexistence of Solutions to Certain Fractional Telegraph Equation

abstract:
We consider the Cauchy problem for the semi-linear fractional telegraph equation
$$
\mathbf{D}_{0\vert t }^{2\gamma }u+\mathbf{D}_{0\vert t }^{\gamma }u+(-\Delta )^{\frac{\beta }{2}}u=h(x,t)\vert u\vert ^{p}
$$
with the given initial data, where ${p}>1$, $\frac{1}{2}\leq \gamma <1$ and $0<\beta <2$. The Nonexistence results and the necessary conditions for global existence are established.

Mathematics Subject Classification: 35L60

Key words and phrases: Critical exponent, fractional power derivative, telegraph equation