Geodesic
Maximum and minimum principles for nonlinear transport equations on discrete-space domains
Electronic Journal of Differential Equations, Tome 2014 (2014).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 82C70, 34A33, 35B50
Keywords: nonlinear transport equation, discrete-space domain, maximum principles, existence, uniqueness, sign preservation, uniform stability, nonlinear comparison theorem 
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     author = {Volek, Jonas},
     title = {Maximum and minimum principles for nonlinear transport equations on discrete-space domains},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2014},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a74/}
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Volek, Jonas. Maximum and minimum principles for nonlinear transport equations on discrete-space domains. Electronic Journal of Differential Equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a74/