Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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

   
 

 

On the question of global existence for reaction-diffusion systems with mixed boundary conditions


Author: Selwyn L. Hollis
Journal: Quart. Appl. Math. 51 (1993), 241-250
MSC: Primary 35K57; Secondary 35B35, 35K55
DOI: https://doi.org/10.1090/qam/1218366
MathSciNet review: MR1218366
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The question of global existence for solutions of reaction-diffusion systems presents fundamental difficulties in the case in which some components of the system satisfy Neumann boundary conditions while others satisfy nonhomogeneous Dirichlet boundary conditions. We discuss particular examples for which classical solutions are known to exist globally when all components satisfy the same type of boundary condition and yet either finite-time blowup occurs or else global existence is unknown when mixed boundary condition types are imposed on the system. Some positive results are presented concerning global existence in the presence of mixed boundary conditions if certain structure requirements are placed on the system, and these results are applied to some particular chemical reaction models.


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


Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 35K57, 35B35, 35K55

Retrieve articles in all journals with MSC: 35K57, 35B35, 35K55


Additional Information

DOI: https://doi.org/10.1090/qam/1218366
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