Existence, uniqueness and bounds for a problem in combustion theory

Mohammed Al-Refai

doi:10.1016/j.cam.2003.10.023

Existence, uniqueness and bounds for a problem in combustion theory

Mohammed Al-Refai

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

A problem in combustion theory consisting of a nonlinear elliptic equation and linear boundary condition is considered. The existence of a non-negative solution is proved and a sufficient condition is given for the uniqueness. Upper and lower bounds for the solutions are obtained by solving linear elliptic equations. These bounds are used as initial functions for an iterative scheme to improve them. Comparison with previous results is obtained whenever possible.

Original language	English
Pages (from-to)	255-269
Number of pages	15
Journal	Journal of Computational and Applied Mathematics
Volume	167
Issue number	2
DOIs	https://doi.org/10.1016/j.cam.2003.10.023
Publication status	Published - Jun 1 2004
Externally published	Yes

Keywords

Combustion theory
Comparison theory
Elliptic equations

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.cam.2003.10.023

Cite this

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abstract = "A problem in combustion theory consisting of a nonlinear elliptic equation and linear boundary condition is considered. The existence of a non-negative solution is proved and a sufficient condition is given for the uniqueness. Upper and lower bounds for the solutions are obtained by solving linear elliptic equations. These bounds are used as initial functions for an iterative scheme to improve them. Comparison with previous results is obtained whenever possible.",

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AB - A problem in combustion theory consisting of a nonlinear elliptic equation and linear boundary condition is considered. The existence of a non-negative solution is proved and a sufficient condition is given for the uniqueness. Upper and lower bounds for the solutions are obtained by solving linear elliptic equations. These bounds are used as initial functions for an iterative scheme to improve them. Comparison with previous results is obtained whenever possible.

KW - Combustion theory

KW - Comparison theory

KW - Elliptic equations

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EP - 269

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 2

ER -

Existence, uniqueness and bounds for a problem in combustion theory

Abstract

Keywords

ASJC Scopus subject areas

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