任意正初始能量状态下半线性波动方程解的有限时间爆破

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Finite Time Blow-Up for the Damped Semilinear Wave Equations with Arbitrary Positive Initial Energy

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Abstract: This paper investigates the initial-boundary value problem of the semilinear wave equation with strong damped terms. We provide the sufficient conditions of finite time blow-up of solutions with high initial energy under some reasonable restrictions on the initial data. In the case of the arbitrary positive initial energy, we also present the sufficient conditions of the existence of global solutions in the energy space.

Key words: Damped wave equations, High initial energy, Blow-up, Global existence

CLC Number:

O175

Su Xiao, Wang Shubin. Finite Time Blow-Up for the Damped Semilinear Wave Equations with Arbitrary Positive Initial Energy[J].Acta mathematica scientia,Series A, 2017, 37(6): 1085-1093.

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