Global nonexistence of solutions for a quasilinear wave equation with acoustic boundary conditions
Global nonexistence of solutions for a quasilinear wave equation with acoustic boundary conditions
We consider the quasilinear wave equation $$u_{tt} -\triangle u_{t} -\operatorname{div}\bigl(\vert \nabla u\vert ^{\alpha-2} \nabla u\bigr) - \operatorname{div}\bigl(\vert \nabla u_{t}\vert ^{\beta-2} \nabla u_{t} \bigr) +a \vert u_{t}\vert ^{m-2} u_{t} =b|u|^{p-2} u $$ $a,b>0$ , associated with initial and Dirichlet boundary conditions at one part and acoustic boundary conditions at another part, …