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International Journal of Mathematics and Mathematical Sciences
Volume 23, Issue 2, Pages 81-88
http://dx.doi.org/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 Hindawi Publishing Corporation. 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.