Vacuum isolating and blow-up analysis for edge hyperbolic system on edge Sobolev spaces

Authors: MORTEZA KOOZEHGAR KALLEJI, NEMATOLLAH KADKHODA

Abstract: This paper deals with the study of the initial-boundary value problem of edge-hyperbolic system with damping term on the manifold with edge singularity. More precisely, it is analyzed the invariance and vacuum isolating of the solution sets to the edge-hyperbolic systems on edge Sobolev spaces. Then, by using a family of modified potential wells and concavity methods, it is obtained existence and nonexistence results of global solutions with exponential decay and is shown the blow-up in finite time of solutions on the manifold with edge singularities.

Keywords: Semilinear hyperbolic equation, potential wells, cone Sobolev spaces, partial differential operator

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