Blow-up in a reactive-diffusive medium with a moving heat source

Authors:
C. M. Kirk;W. E. Olmstead
Affiliations:
Department of Mathematics, California Polytechnic State University, San Luis Obispo, CA;Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL
Venue:
Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
Year:
2002

Citing 5
Cited 5

The role of critical exponents in blowup theorems

SIAM Review
A thermal explosion model

Applied Mathematics and Computation
Blow-up rates for parabolic systems

Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
Critical speed for the avoidance of blow-up in a reactive-diffusive medium

Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
The influence of two moving heat sources on blow-up in a reactive-diffusive medium

Zeitschrift für Angewandte Mathematik und Physik (ZAMP)

Recent results on blow-up and quenching for nonlinear Volterra equations

Journal of Computational and Applied Mathematics
Moving mesh methods for blowup in reaction-diffusion equations with traveling heat source

Journal of Computational Physics
A numerical investigation of blow-up in reaction-diffusion problems with traveling heat sources

Journal of Computational and Applied Mathematics
An adaptive splitting approach for the quenching solution of reaction-diffusion equations over nonuniform grids

Journal of Computational and Applied Mathematics
Solving degenerate quenching-combustion equations by an adaptive splitting method on evolving grids

Computers and Structures

Quantified Score

Hi-index	0.01

Visualization

Abstract

A concentrated source of heat is allowed to move in one-dimension through a reactive-diffusive medium. For rather general motion, it is shown that if the speed remains sufficiently high then a blow-up can be avoided; whereas, if the speed remains sufficiently low then a blowup must eventually occur. Other criteria involving the displacement and velocity of the heat source are found to guarantee a blow-up. Special examples of (i) rapid deceleration from one velocity level to a lower level and (ii) a simple periodic motion are examined.