On closed-form solutions of some nonlinear partial differential equations
S. S. Okoya1
Received12 Jun 1995
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.