Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 

 

The thermistor problem for conductivity which vanishes at large temperature


Authors: Xinfu Chen and Avner Friedman
Journal: Quart. Appl. Math. 51 (1993), 101-115
MSC: Primary 35R35; Secondary 35J45, 80A20
DOI: https://doi.org/10.1090/qam/1205940
MathSciNet review: MR1205940
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The thermistor problem is modeled as a coupled system of nonlinear elliptic equations. When the conductivity coefficient $ \sigma \left( u \right)$ vanishes ($ u$ = temperature) one of the equations becomes degenerate; this situation is considered in the present paper. We establish the existence of a weak solution and, under some special Dirichlet and Neumann boundary conditions, analyze the structure of the set $ \left\{ {\sigma \left( u \right) = 0} \right\}$ and also prove uniqueness.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 35R35, 35J45, 80A20

Retrieve articles in all journals with MSC: 35R35, 35J45, 80A20


Additional Information

DOI: https://doi.org/10.1090/qam/1205940
Article copyright: © Copyright 1993 American Mathematical Society


Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2017 Brown University
Comments: qam-query@ams.org
AMS Website