一类高阶波动方程的整体解及指数衰减估计

Abstract

Abstract: This paper deals with the initial-boundary value problem for a class of higher-order nonlinear wave equation with strong dissipative term in a bounded domain. We prove the existence of global solutions for this problem by constructing a stable set in H₀^m(Ω) and give the exponential decay estimate. Meanwhile, the blow-up result of solution in the unstable set is also obtained if the initial energy is positive.

Key words: Nonlinear higher-order wave equation, Initial-boundary value problem, Strong dissipative term, Global solution, Exponential decay

CLC Number:

O175.2

Ye Yaojun, Hu Yue. Global Existence and Exponential Decay of Solution for Some Higher-Order Wave Equation[J].Acta mathematica scientia,Series A, 2018, 38(1): 110-121.

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Global Existence and Exponential Decay of Solution for Some Higher-Order Wave Equation

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