N维外区域中带变系数非线性项的半线性波动方程解的爆破

Abstract

Abstract:

In this paper, we are concerned with the N(N ≥ 2)-dimensional exterior problem for a class of semilinear wave equations with variable coefficient nonlinearity. We mainly consider the blow up and lifespan of the solutions. Base on [19-20], by utilizing the test function and the harmonic functions of N=2 and N ≥ 3 in the exterior domains with Dirichlet boundary condition, we are able to derive the upper bound of lifespan. In particular, the impact of the variable coefficient nonlinearity on the lifespan has been discussed in detail.

Key words: Semilinear wave equation, Exterior domain, Blow up, Life estimate

CLC Number:

O175.2

Shoujun Huang,Juan Wang. Blow up of Solutions to Semilinear Wave Equations with Variable Coefficient for Nonlinearity in an N-Dimensional Exterior Domain[J].Acta mathematica scientia,Series A, 2020, 40(5): 1259-1268.

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References 20

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Blow up of Solutions to Semilinear Wave Equations with Variable Coefficient for Nonlinearity in an N-Dimensional Exterior Domain

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