Existence and Blow-up for a Parabolic System from Combustion Theory

We study the stability of the Solid Fuel Model , which represents a thermal reaction of a solid material. This model corresponds to a nonlinear eigenvalue problem of two strongly coupled nonlinear reaction–diffusion equations, with different boundary conditions on each unknown. We obtain a strong bi...

Full description

Saved in:
Bibliographic Details
Published in:Journal of nonlinear science 2011-08, Vol.21 (4), p.563-578
Main Authors: Arancibia, Alejandro Omón, Barrera, Andrés Avila
Format: Article
Language:English
Subjects:
Analysis
Classical Mechanics
Economic Theory/Quantitative Economics/Mathematical Methods
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We study the stability of the Solid Fuel Model , which represents a thermal reaction of a solid material. This model corresponds to a nonlinear eigenvalue problem of two strongly coupled nonlinear reaction–diffusion equations, with different boundary conditions on each unknown. We obtain a strong bifurcation criterion for the steady problem and estimates for the blow-up time in the unsteady case. In addition, numerical solutions of both the steady and unsteady problem are presented to illustrate the results.
ISSN:0938-8974
1432-1467
DOI:10.1007/s00332-010-9092-8