International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 4, Pages 731-736
doi:10.1155/S0161171291000984
Remarks on quasilinear evolutions equations
1National Laboratory of Scientific Computation, Rua Lauro Muller 455, (LNCC-CNPq) Botafogo, CEP. 22290, Rio de Janeiro, R.J., Brazil
2IMUFRJ , P. O. Box 68530, Rio de Janeiro, R.J., Brazil
Received 6 June 1990; Revised 21 July 1990
Copyright © 1991 James E. Munoz Rivera. 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.
Abstract
In this paper we study the existence result of classical solutions for the quasilinear equation utt−Δu−M(∫Ω|∇u|2dx)Δutt=f, with initial data u(0)=u0, u(1)=u1 and homogeneous boundary conditions.