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On potential wells and vacuum isolating of solutions for semilinear wave equations. (English) Zbl 1024.35078

The author studies the initial boundary value problem of semilinear wave equation \(u_{tt}-\triangle u=|u|^{p-1}u\) on a bounded domain. He introduces a family of potential wells which include the known potential well as a special case, to prove existence and nonexistence theorems of global solutions for the problem.

MSC:

35L70 Second-order nonlinear hyperbolic equations
35L20 Initial-boundary value problems for second-order hyperbolic equations
35B45 A priori estimates in context of PDEs
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