2015/04/08 by Rinaldo M. Colombo, Colombo, Rinaldo M., Elena Rossi +1
Mathematics · #35L50 #35L65 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35L50 #msc:35L65
paper · pdf · doi:10.48550/arxiv.1504.01907
arxiv created 2015/04/08 · arxiv updated 2015/04/09
The initial-boundary value problem for a general balance law in a bounded domain is proved to be well posed. Indeed, we show the existence of an entropy solution, its uniqueness and its Lipschitz continuity as a function of time, of the initial datum and of the boundary datum. The proof follows the general lines in Bardos, Leroux and Nédélec (1979), striving to provide a rigorous treatment and detailed references.