一类非线性高阶波动方程的初边值问题

Acta mathematica scientia,Series A

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Initial Boundary Value Problems for a Class of Nonlinear Wave Equation of Higher Order

Han Xianjun; Chen Guowang

Department of Mathematics, Zhengzhou University, Zhengzhou 450052

Received:2005-11-21 Revised:2007-01-22 Online:2007-08-25 Published:2007-08-25
Contact: Han Xianjun

Abstract

Abstract:
In this paper the initial boundary value problems for a class of nonlinear wave equation
u_tt－a_1^U_xx+a_₂u_x4+a₃u_x4_tt=φ(u_{x ⁾}x+f(u,u_x,u_xxu_xxx,u_x4)

are considered. The existence and uniqueness of the classical global solution are proved. The sufficient conditions of blow-up of solutions are given.

Key words: Nonlinear wave equation of higher order, Initial boundary value
problem, Classical global solution, Blow-up of solution, Green function

CLC Number:

35L35

Han Xianjun; Chen Guowang. Initial Boundary Value Problems for a Class of Nonlinear Wave Equation of Higher Order[J].Acta mathematica scientia,Series A, 2007, 27(4): 624-640.

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Initial Boundary Value Problems for a Class of Nonlinear Wave Equation of Higher Order

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