Well-posedness for the semilinear wave equations with nonlinear damping on manifolds with conical degeneration

2024/11/30 by Liu, Gongwei, Peng, Yi, Li, Peng
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2412.00335

Abstract

This paper deals with a class of semilinear wave equation with nonlinear damping term |u_t|^m-2u_t and nonlinear source term g(x)|u|^p-2u on the manifolds with conical singularities. Firstly, we prove the local existence and uniqueness of the solution by the semigroup method. Secondly, we establish the global existence, the energy decay estimate and the blow-up in finite time of the solution with subcritial (E(0)

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