International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 3, Pages 543-552

On a nonlinear degenerate evolution equation with strong damping

Jorge Ferreira1 and Ducival Carvalho Pereira2

1IM/UFRJ and Univ. Estadual de Maringá, Paraná, Brazil
2UFPA, Belém, Pará, Brazil

Received 26 June 1990; Revised 12 October 1990

Copyright © 1992 Jorge Ferreira and Ducival Carvalho Pereira. 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 consider the nonlinear degenerate evolution equation with strong damping,(*){K(x,t)uttΔuΔut+F(u)=0inQ=Ω×]0,T[u(x,0)=u0,(ku)(x,0)=0inΩu(x,t)=0on=Γ×]0,T[where K is a function with K(x,t)0, K(x,0)=0 and F is a continuous real function satisfying(**)sF(s)0,forallsR,Ω is a bounded domain of Rn, with smooth boundary Γ. We prove the existence of a global weak solution for (*).