On the Dirichlet-Neumann Boundary Problem for Scalar Conservation Laws. Issue 5 (2nd September 2016)

• Record Type: Journal Article
• Authors: Mišur, Marin; Mitrović, Darko; Novak, Andrej
• Is Part Of: Mathematical modelling and analysis. Volume 21:Issue 5(2016)
• Page Start: 685
• Page End: 698
• Publication Date: 2016-09-02
• Subjects: scalar conservation law -- bounded domain -- Dirichlet-Neumann problem -- compensated compactness -- numerical simulations; 35L65 -- 65N99; Mathematical models -- Periodicals; Mathematical models -- Study and teaching -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis -- Problems, exercises, etc -- Periodicals; Mathematical analysis; Mathematical models; Mathematical models -- Study and teaching; Periodicals; Problems and exercises; 511.805
• DOI: 10.3846/13926292.2016.1214187
• Languages: English
• ISSNs: 1392-6292

Abstract

Abstract: We consider a Dirichlet-Neumann boundary problem in a bounded domain for scalar conservation laws. We construct an approximate solution to the problem via an elliptic approximation for which, under appropriate assumptions, we prove that the corresponding limit satisfies the considered equation in the interior of the domain. The basic tool is the compensated compactness method. We also provide numerical examples.