Journal of East China Normal University(Natural Sc ›› 2009, Vol. 2009 ›› Issue (4): 78-81.

• Article • Previous Articles     Next Articles

Solutions to a linear wave equation with nonlinear\\[5pt] boundary conditions

WANG Li-hua1, 2   

  1. 1. {\it Department of Mathematics, East China Normal University, Shanghai} 200062, {\it China}

    2. {\it

    Department of Basic Courses, Suzhou Vocational University, Suzhou Jiangsu}215104, {\it China

  • Received:2008-09-06 Revised:2008-12-06 Online:2009-07-25 Published:2009-07-25
  • Contact: WANG Li-hua1

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Abstract:

This paper was concerned with a one-dimensional linear wave equation
associated with nonlinear boundary conditions. The unique local solution to the wave
equation was proved to exist. The result is that the nonlinearity at the boundary causes
a finite time blow up of the solution, even for small initial data. And the upper bound
to the blow up time is given in the paper

Key words: local existence, blow up, wave equation, local existence, blow up

CLC Number: