Acta mathematica scientia,Series A ›› 2009, Vol. 29 ›› Issue (4): 1093-1103.

• Articles • Previous Articles     Next Articles

Blow-up of |Solutions |of |an |Initial |Boundary |Value Problem for a Class of Nonlinear Wave Equation

  

  1. (Department of Mathematics and Physics, Zhengzhou Institute of Aeronautical Industry Management, Zhengzhou 450015)
  • Received:2007-03-22 Revised:2008-09-12 Online:2009-08-25 Published:2009-08-25
  • Supported by:

    国家自然科学基金(10671182)、河南省高等学校青年骨干教师资助计划项目(2006110016)资助

Abstract:

In this paper, the following initial boundary value problem  of the nonlinear wave equation involving the nonlinear damping term and the
nonlinear source term
utt -uxxt -uxx -(σ(u2x)ux)x+δ|ut|p-1ut=μ|u|q-1u, 0 < x <1, 0 ≤ t ≤ T,      
u(0, t)=u(1, t)=0,  0 ≤ t ≤ T,                                                                     

u(x, 0)=u0(x),  ut(x, 0)=u1(x), 0 ≤ x ≤1                                           
is discussed. This paper gives sufficient conditions of  blow-up of the solutions for the problem in finite time and proves the existence and uniqueness of the local generalized solution and classical solution of this problem.

Key words: Nonlinear wave equation, Initial boundary value problem, Local solution, Blow-up of solution

CLC Number: 

  • 35L35
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