Blowup of solutions of a nonlinear wave equation
Summary: We establish a blowup result to the initial-boundary value problem \[ \begin{matrix} {\l}\qquad & {\l}\\ u_{tt}-Au+ku_t=|u|^{p-2}u, & x\in\Omega,\;t>0,\\ u(x,t)=0, & x\in\partial\Omega,\;t\geq 0,\\ u(x,0)=u_0(x), \quad u_t(x,0)=u_1(x), & x\in \Omega,\end{matrix} \] where \[ Au=M\left(\|B^{1/2}u\|^2\right)e^{-\phi(x)} \text{div}(e^{\phi(x)}\nabla u), \] \[ \|B^{1/2}u\|^2 = \int_\Omega e^{\Phi(x)}|\nabla u|^2 dx, \] \(p > 2\) is a constant, \(k\) is a positive constant, \(M: \mathbb{R}^+\to \mathbb{R}^+\) is a continuous function, \(\Phi\in L^\infty(\Omega)\), and \(\Omega\subset\mathbb{R}^n\) is a bounded domain with a smooth boundary.
scientific article; zbMATH DE number 1780544