Asymptotic behavior of solutions of some nonlinearly damped wave equations on $\mathbb R^N$
Asymptotic behavior of solutions of some nonlinearly damped wave equations on $\mathbb R^N$
We discuss the asymptotic behavior of solutions of the nonlinearly damped wave equation $$ u_{tt} +\delta \vert u_t\vert ^{m-1}u_t -\phi (x)\Delta u = \lambda u\vert u\vert ^{\beta -1}, \quad x \in \mathbb R^n, \ t \geq 0, $$ with the initial conditions $ u(x,0) = u_0 (x)$ and $u_t(x,0) = …