具阻尼的高维广义Boussinesq 方程的Cauchy 问题的整体适定性

Abstract

Abstract:

We study the Cauchy problem for a class of damped multidimensional generalized Boussinesq equations u_tt-Δu-Δu_tt+Δ²u- kΔu_t=Δf(u), where k>0. By using potential well method, we analyze the relation between the coefficient k of damping term and the initial data as well as the depth of potential well and obtain the existence and nonexistence of global
weak solution without establishing the local existence theory.

Key words: Damped multidimensional generalized Boussinesq equations, Cauchy problem, Global existence, Nonexistence, Potential well method

CLC Number:

35L75

SHEN Ji-Hong, ZHANG Ming-You, YANG Yan-Bing, LIU Bo-Wei, XU Run-Zhang. Global Well-posedness of Cauchy Problem for Damped Multidimensional Generalized Boussinesq Equations[J].Acta mathematica scientia,Series A, 2014, 34(5): 1173-1187.

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References

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Global Well-posedness of Cauchy Problem for Damped Multidimensional Generalized Boussinesq Equations

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