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Global results for semilinear hyperbolic equations with damping term on manifolds with conical singularity. (English) Zbl 1387.35417

Summary: In this paper, we apply the family of potential wells to the initial boundary value problem of semilinear hyperbolic equations on the cone Sobolev spaces. We not only give some results of global existence and nonexistence of solutions but also obtain the vacuum isolating of solutions. Finally, we show blow-up in finite time of solutions on a manifold with conical singularities.

MSC:

35L71 Second-order semilinear hyperbolic equations
47F05 General theory of partial differential operators
35L20 Initial-boundary value problems for second-order hyperbolic equations
35B44 Blow-up in context of PDEs
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