Critical behaviour of nonlinear elliptic boundary value problems suggested by exothermic reactions

Author:

Wiebers Henning

Abstract

SynopsisWe consider a class of semilinear elliptic boundary value problems depending on a parameter, which arise in the theory of combustion. Based on the results in another paper by the same author, a rigorous quantitative connection is shown between the solution set of the boundary value problem and that of a simple scalar equation (the Semenov approximation).

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference17 articles.

1. 17 Wiebers H. . A uniqueness result for a nonlinear two point boundary value problem. Nonlinear Anal, submitted.

2. 15 Wiebers H. . S-formige Verzweigungsdiagramme bei elliptischen Randwertaufgaben mit Anwendungen auf exotherme Reaktionen. Ph.D. thesis, Hamburg 1984.

3. S-Shaped bifurcation curves of nonlinear elliptic boundary value problems

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1. Bifurcation curves in a combustion problem with general Arrhenius reaction-rate laws;ANNALI DELL'UNIVERSITA' DI FERRARA;2016-07-29

2. Bifurcation and Related Topics in Elliptic Problems;Handbook of Differential Equations: Stationary Partial Differential Equations;2005

3. Semilinear elliptic boundary-value problems in combustion theory;Proceedings of the Royal Society of Edinburgh: Section A Mathematics;2002-12

4. Bifurcation from Infinity for Asymptotically Linear Elliptic Eigenvalue Problems;Journal of Mathematical Analysis and Applications;2002-03

5. Equations of Gas Combustion: S-Shaped Bifurcation and Mushrooms;Journal of Differential Equations;1997-03

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