Global existence and nonexistence of semilinear wave equation with a new condition

Abstract

In this paper, we consider the initial-boundary problem for semilinear wave equation with a new condition $$\alpha {\int }_0^{u}f(s)ds\le uf(u)+\beta u^2+\alpha \sigma ,$$ for some positive constants $\alpha$, $\beta$, and $\sigma$, where $\beta <\frac{{\lambda }_1(\alpha -2)}{2}$ with ${\lambda }_1$ being a first eigenvalue of Laplacian. By introducing a family of potential wells, we establish the invariant sets, vacuum isolation of solutions, global existence and blow-up solutions of semilinear wave equation for initial conditions $E(0)<d$ and $E(0)=d$.

arXiv admin note: text overlap with arXiv:2104.06896

References in corpus (1)

• A New Condition for the Concavity Method of Blow-up Solutions to p-Laplacian Parabolic Equations