On closed-form solutions of some nonlinear partial differential equations
type: Item
instance of: scholarly article
title: On closed-form solutions of some nonlinear partial differential equations
zbMATH Open document ID: 1021.35024
DOI: 10.1155/S0161171200001289
author: Samuel S. Okoya
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2003-10-20T00:00:00Z
full work available at URL: https://eudml.org/doc/50323
review text: 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.
Mathematics Subject Classification ID: 35C05
Mathematics Subject Classification ID: 80A25
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 1441867
zbMATH Keywords: exothermic reaction
zbMATH Keywords: endothermic reaction
zbMATH Keywords: large activation energy
zbMATH Keywords: steady state thermal explosion
MaRDI profile type: Publication
OpenAlex ID: W2111105372
description: scientific article; zbMATH DE number 1441867