Abstract
This paper reviews the recent work on the global weak entropy solutions of scalar conservation laws with boundary effect and the global error estimate for viscosity methods to initial-boundary value problems of scalar conservation laws. In section 2, we state how to obtain the existence of weak entropy solution for general nonconvex scalar conservation laws by Dafermos’s polygonal approximations method which can be used to simulate geometric structure of the weak entropy solution. We also state the large time behaviors of weak entropy solution by discussing the interaction of elementary waves for scalar convex conservation laws on a bounded domain. In section 3, we are concerned with the global error estimate for viscous approximations to inviscid solution to initial-boundary value problems of convex scalar conservation laws by the matching traveling wave solutions method.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
