带粘性的波动方程组解的逐点估计

Abstract

Abstract:

The Cauchy problem for two systems of wave equations with viscosity in dimension three is considered. By using the long wave and short wave decomposition method together with energy method and Green function, the pointwise estimates of the time-asymptotic shape of the solution are given, which exhibit two kinds of generalized Huygens' waves. As a byproduct, the optimal L^p-decay rates with p ≥ 1 of the solutions of these systems are also established.

Key words: Green function, Systems of wave equations with viscosity, Huygens' principle

CLC Number:

O175.2

Zhigang Wu,Xiaofang Miao. Pointwise Estimates for Systems of Wave Equations with Viscosity[J].Acta mathematica scientia,Series A, 2019, 39(6): 1421-1442.

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Pointwise Estimates for Systems of Wave Equations with Viscosity

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