一类带有非线性阻尼项和源项的四阶波动方程整体解的存在性与不存在性

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Global Existence and Nonexistence of Solutions for A Class of Fourth Order Wave Equation with Nonlinear Damping and Source Terms

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Abstract:

In this paper, we consider the initial boundary value problem of the fourth order wave equation with nonlinear damping and source terms. By the combination of Galerkin approximations, Potential well and Monotonicity-Compactness methods, the global existence of solutions is obtained with the least amount of a priori estimates. Moreover, we prove that there are solutions with negative initial energy that blow up in finite time.

Key words: Wave equation, Global existence, Blow up, Damping and source terms, Monotonicity-Compactness methods

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O175.4

Di Huafei, Shang Yadong. Global Existence and Nonexistence of Solutions for A Class of Fourth Order Wave Equation with Nonlinear Damping and Source Terms[J].Acta mathematica scientia,Series A, 2015, 35(3): 618-633.

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