On closed-form solutions of some nonlinear partial differential equations (Q1975935)
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scientific article; zbMATH DE number 1441867
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On closed-form solutions of some nonlinear partial differential equations |
scientific article; zbMATH DE number 1441867 |
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On closed-form solutions of some nonlinear partial differential equations (English)
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20 October 2003
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Summary: This paper is devoted to closed-form solutions of the partial differential equation: \(\theta_{xx} + \theta_{yy} + \delta\exp(\theta)= 0\), which arises in the steady state thermal explosion theory. We find simple exact solutions of the form \(\theta(x,y) = \Phi(F(x) +G(y))\), and \(\theta(x,y) = \Phi(f(x +y)+g(x -y))\). Also, we study the corresponding nonlinear wave equation.
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exothermic reaction
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endothermic reaction
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large activation energy
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steady state thermal explosion
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