International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 1, Pages 151-160

Existence of solutions for a nonlinear hyperbolic-parabolic equation in a non-cylinder domain

Marcondes Rodrigues Clark

Universidade Federal Da Paraíba, Departamento De Matemátics E Estatistica, Campus II- 58, Campina Grande 109-970, PB, Brazil

Received 18 June 1993; Revised 1 December 1993

Copyright © 1996 Marcondes Rodrigues Clark. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper, we study the existence of global weak solutions for the equationk2(x)u+k1(x)u+A(t)u+|u|ρu=f(I)in the non-cylinder domain Q in Rn+1; k1 and k2 are bounded real functions, A(t) is the symmetric operatorA(t)=i,j=1nxj(aij(x,t)xi)where aij and f are real functions given in Q. For the proof of existence of global weak solutions we use the Faedo-Galerkin method, compactness arguments and penalization.