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Comparison and maximum principles for a class of flux-limited diffusions with external force fields
- Source :
- Advances in Nonlinear Analysis, Vol 5, Iss 2, Pp 167-176 (2016)
- Publication Year :
- 2016
- Publisher :
- De Gruyter, 2016.
-
Abstract
- In this paper, we are interested in a general equation that has finite speed of propagation compatible with Einstein's theory of special relativity. This equation without external force fields has been derived recently by means of optimal transportation theory. We first provide an argument to incorporate the external force fields. Then we are concerned with comparison and maximum principles for this equation. We consider both stationary and evolutionary problems. We show that the former satisfies a comparison principle and a strong maximum principle. While the latter fulfils weaker ones. The key technique is a transformation that matches well with the gradient flow structure of the equation.<br />Comment: 15 pages. Comments are welcome
- Subjects :
- Class (set theory)
Structure (category theory)
Mathematics, Applied
Flux
FOS: Physical sciences
Transportation theory
01 natural sciences
35j62
FLOWS
symbols.namesake
Mathematics - Analysis of PDEs
Maximum principle
35k59
35q75
CONVERGENCE
FOKKER-PLANCK EQUATION
FOS: Mathematics
0101 mathematics
Einstein
Mathematical Physics
Mathematics
QA299.6-433
Science & Technology
flux-limited diffusions
010102 general mathematics
Mathematical analysis
Mathematical Physics (math-ph)
relativistic heat equations
010101 applied mathematics
Transformation (function)
QUASI-LINEAR EQUATION
Physical Sciences
symbols
Balanced flow
comparison and maximum principles
Analysis
Analysis of PDEs (math.AP)
Subjects
Details
- Language :
- English
- ISSN :
- 21919496
- Volume :
- 5
- Issue :
- 2
- Database :
- OpenAIRE
- Journal :
- Advances in Nonlinear Analysis
- Accession number :
- edsair.doi.dedup.....41e4da8324806222f0b659c872c85d6a