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Global results for semilinear hyperbolic equations with damping term on manifolds with conical singularity
Author(s) -
Alimohammady Mohsen,
Koozehgar Kalleji Morteza,
Karamali Gholamreza
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4295
Subject(s) - mathematics , conical surface , gravitational singularity , sobolev space , singularity , term (time) , manifold (fluid mechanics) , initial value problem , mathematical analysis , cone (formal languages) , boundary value problem , boundary (topology) , hyperbolic partial differential equation , hyperbolic manifold , pure mathematics , hyperbolic function , partial differential equation , geometry , physics , quantum mechanics , mechanical engineering , algorithm , engineering
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. Copyright © 2017 John Wiley & Sons, Ltd.