一类具对数源项波动方程的初边值问题

Abstract

Abstract:

In this paper we consider the initial boundary value problem for a class wave equation with logarithmic source term. By using Galerkin method combining with the logarithmic Sobolev inequality and logarithmic Gronwall inequality, we obtain the existence of global solution for all initial data. By introducing potential well theory, we give the sufficient condition of the blow-up property in infinity time (i.e. exponential growth) of the solution. By constructing an appropriate Lyapunov function, we obtain the decay estimates of energy for the wave equation with logarithmic source term and linear damping term.

Key words: Logarithmic wave equation, Existence of global solution, Exponential growth, Decay

CLC Number:

O175.4

Zhang Hongwei, Liu Gongwei, Hu Qingying. Initial Boundary Value Problem for a Class Wave Equation with Logarithmic Source Term[J].Acta mathematica scientia,Series A, 2016, 36(6): 1124-1136.

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References

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Initial Boundary Value Problem for a Class Wave Equation with Logarithmic Source Term

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