International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 2, Pages 81-88
doi:10.1155/S0161171200001289
On closed-form solutions of some nonlinear partial differential equations
Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Nigeria
Received 12 June 1995
Copyright © 2000 S. S. Okoya. 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
This paper is devoted to closed-form solutions of the partial
differential equation: θxx+θyy+δexp(θ)=0, which arises in the steady state thermal explosion
theory. We find simple exact solutions of the form θ(x,y)=Φ(F(x)+G(y)), and θ(x,y)=Φ(f(x+y)+g(x-y)). Also, we study the corresponding nonlinear wave equation.