Remarks on the semilinear wave equations. (English) Zbl 0965.35096
Summary: We study the semilinear wave equation of the form:
\[
\square u+ u_t+|u_t|^{p-1} u_t= |u|^{q-1}u.
\]
When \(1< q\leq p\), a solution exists globally in all time and when \(1< p< q\), the local solution blows up in finite time for negative initial energy.
MSC:
35L70 | Second-order nonlinear hyperbolic equations |
35L20 | Initial-boundary value problems for second-order hyperbolic equations |
35B40 | Asymptotic behavior of solutions to PDEs |