Full paper in PDF:
$%J.-P. Dias and M. Figueira, A remark on the blow-up of the solutions of the equation ut+ f(x)a(u)ux = h(x,u)  , Rev. Mat. Univ. Complut. Madrid 9 (1996), no. 2, 385391.%$

A Remark on the Blow-Up of the Solutions of the Equation ut +  f (x)a(u)ux      =  h(x,  u)
João-Paulo DIAS and Mário FIGUEIRA
CMAF/University of Lisbon
2 Av. Prof. Gama Pinto
1699 Lisboa Codex Portugal

Received: October 23, 1995
 
ABSTRACT

We consider the Cauchy problem for the equation ut+ f(x)a(u)ux = h(x,u)  where f  , a  , and h  are real C1  functions, f > h > 0  , a'> 0  , hu> 0  and hx < 0  . Following the ideas of Lax (1964) and Klainerman-Majda (1980), we prove a blow-up result for the solutions with special data corresponding, in certain cases, to the development of a singularity in ux  .

1991 Mathematics Subject Classification: 35L65, 35L67.