Finite Propagation Speed for Limited Flux Diffusion Equations

We prove that the support of solutions of a limited flux diffusion equation known as a relativistic heat equation evolves at a constant speed, identified as the speed of light c. For that we construct entropy sub- and super-solutions which are fronts evolving at speed c and prove the corresponding c...

Full description

Saved in:
Bibliographic Details
Published inArchive for rational mechanics and analysis Vol. 182; no. 2; pp. 269 - 297
Main Authors Andreu, Fuensanta, Caselles, Vicent, Mazón, José M., Moll, Salvador
Format Journal Article
LanguageEnglish
Published Heidelberg Springer Nature B.V 01.10.2006
Subjects
Studies
Online AccessGet full text

Cover

More Information
Summary:We prove that the support of solutions of a limited flux diffusion equation known as a relativistic heat equation evolves at a constant speed, identified as the speed of light c. For that we construct entropy sub- and super-solutions which are fronts evolving at speed c and prove the corresponding comparison principle between entropy solutions and sub- and super-solutions, respectively. This enables us to prove the existence of discontinuity fronts moving at light's speed.[PUBLICATION ABSTRACT]
ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-006-0428-3