Critical exponent for semi-linear structurally damped wave equation of derivative type

Abstract

Main purpose of this paper is to study the following semi-linear structurally damped wave equation with nonlinearity of derivative type: $$u_{tt}-\Delta u+\mu (-\Delta {)}^{\sigma /2}{u}_t=|u_t{|}^p,u(0,x)=u_0(x),u_t(0,x)=u_1(x),$$ with $\mu >0$, $n\ge 1$, $\sigma \in (0,2]$ and $p>1$. In particular, we are going to prove the non-existence of global weak solutions by using a new test function and suitable sign assumptions on the initial data in both the subcritical case and the critical case.

arXiv comment9 pages

References in corpus (4)

• Ten equivalent definitions of the fractional Laplace operator
• Semi-linear structural damped waves
• Blow up results for semi-linear structural damped wave model with nonlinear memory
• A blow-up result for semi-linear structurally damped $\sigma$-evolution equations

Cited by in corpus (1)

• Parabolic problems whose Fujita critical exponent is not given by scaling