ON CLOSED-FORM SOLUTIONS OF SOME NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS

This paper is devoted to closed-form solutions of the partial differential equation: θ_(xx) +θ_(yy) +δ_(exp)(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 corresp...

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Bibliographic Details
Published in:International Journal of Mathematics and Mathematical Sciences 2000-01, Vol.2000 (2), p.81-88-011
Main Author: Okoya, S. S.
Format: Article
Language:English
Subjects:
endothermic reaction
exothermic reaction
large activation energy
Thermal explosion theory
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Summary:This paper is devoted to closed-form solutions of the partial differential equation: θ_(xx) +θ_(yy) +δ_(exp)(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.
ISSN:0161-1712
1687-0425
DOI:10.1155/S0161171200001289