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

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.