Electronic Journal of Differential Equations,
Conf. 10 (2002), pp. 23-31.

Title: An adaptive numerical method for the wave equation
       with a nonlinear boundary condition

Authors: Azmy S. Ackleh (Univ. of Louisiana at Lafayette, USA)
 Keng Deng (Univ. of Louisiana at Lafayette, USA)
 Joel Derouen (Univ. of Louisiana at Lafayette, USA)
 
Abstract: 
 We develop an efficient numerical method for
 studying the existence and non-existence of global solutions to the
 initial-boundary value problem
 \begin{gather*}
 u_{tt}=u_{xx}\quad  0<x<\infty,\;  t>0,\\
 -u_{x}(0,t)=h(u(0,t)) \quad t>0,\\
 u(x,0)=f(x),\quad u_{t}(x,0)=g(x) \quad 0<x<\infty.
 \end{gather*}
 The results by this numerical method corroborate the theory presented in
 \cite{AD}. Furthermore, they suggest that blow-up can occur for more general
 nonlinearities $h(u)$ with weaker conditions on the initial data
 $f$ and $g$.


Published February 28, 2003.
Math Subject Classifications: 35B40, 35L05, 35L20, 65M25, 65N50.
Key Words: Time-adaptive numerical method; blow-up time; blow-up rate.