International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 1, Pages 151-160
doi:10.1155/S0161171296000221

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

Abstract

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=1n∂∂xj(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.