Non-existence of solutions for a Timoshenko equations with weak dissipation. (English) Zbl 1474.35006
Summary: In this paper, we consider the following Timoshenko equation
\[
u_{tt}+\triangle^2u-M\left( \left\Vert \nabla u\right\Vert^2\right) \triangle u+u_t=\left\vert u\right\vert^{q-1}u
\]
associated with initial and Dirichlet boundary condition. We prove that the non-existence of solutions with positive and negative initial energy.
MSC:
35A01 | Existence problems for PDEs: global existence, local existence, non-existence |