International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 2, Pages 335-342
doi:10.1155/S0161171288000390
On a nonlinear wave equation in unbounded domains
Carlos Frederico Vasconcellos
Instituto de Matemática, Universidade Federal do Rio de Janeiro, P.O. Box 68530, Rio de JaJeiro, RJ CEP 21944, Brazil
Abstract
We study existence and uniqeness of the nonlinear wave equation∂2u∂t2+M(x,∫|∇u(x,t)|2dx+∫|u(x,t)|2dx)(−Δu+u)=0in unbounded domains. The above model describes nonlinear wave phenomenon in non-homogeneous media. Our techniques ivolve fixed point arguments combined with the energy method.