Maximum and minimum principles for nonlinear transport equations on discrete-space domains
We consider nonlinear scalar transport equations on the domain with discrete space and continuous time. As a motivation we derive a conservation law on these domains. In the main part of the paper we prove maximum and minimum principles that are later applied to obtain an a priori bound whi...
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| Format: | Article |
| Language: | English |
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Texas State University
2014-03-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2014/78/abstr.html |
| Summary: | We consider nonlinear scalar transport equations on the domain with discrete
space and continuous time. As a motivation we derive a conservation law
on these domains. In the main part of the paper we prove maximum and
minimum principles that are later applied to obtain an a priori bound
which is applied in the proof of existence of solution and its uniqueness.
Further, we study several consequences of these principles such as
boundedness of solutions, sign preservation, uniform stability and
comparison theorem which deals with lower and upper solutions. |
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| ISSN: | 1072-6691 |