Jonas Volek
Abstract:
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.
Submitted December 30, 2013. Published March 19, 2014.
Math Subject Classifications: 82C70, 34A33, 35B50.
Key Words: Nonlinear transport equation; discrete-space domain;
maximum principles; existence; uniqueness; sign preservation;
uniform stability; nonlinear comparison theorem.
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Jonas Volek Department of Mathematics and NTIS New Technologies for the Information Society - European Centre of Excellence Faculty of Applied Sciences, University of West Bohemia in Pilsen Univerzitni 8, 306 14 Pilsen, Czech Republic email: volek1@kma.zcu.cz |
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