Abstract
We consider a scalar balance law with a strict convex flux. In this paper, we study inviscid limit to shocks for scalar balance laws up to a shift function, which is based on the relative entropy.
Highlights
We consider the following balance law in one-dimensional space R:∂tU + ∂xA (U) = g (U) + ε∂x2xU,U (0, x) = U0 (x), (1)t > 0, x ∈ R, where the flux A(V) := a(V) ≥ c for some constant c > 0 and U0 ∈ L∞(R)
The relative entropy method introduced by Dafermos [3, 4] and Diperna [5] provides an efficient tool to study the stability and asymptotic limits among thermomechanical theories, which is related to the second law of thermodynamics
For the relaxation there is an application for compressible models by Lattanzio and Tzavaras [16, 17] and we can see Berthelin et al [18, 19] as some applications of hydrodynamical limit problems
Summary
We consider the following balance law in one-dimensional space R:. t > 0, x ∈ R, where the flux A(V) := a(V) ≥ c for some constant c > 0 and U0 ∈ L∞(R). We consider the following balance law in one-dimensional space R:. We are interested in getting the optimal rate of convergence linked to a layer. Let us consider the shock solutions of the scalar conservation laws with the given source term (1) with the initial data. With two constants CL > CR, where the source term g is defined as follows:. For any convex functions η, and G = ηA. An easy dimensional analysis shows that, because of those layers, we may have in general. For some ε > 0 which means that the L2 stability for two solutions U, S does not hold. We are interested in deriving the extremal L2 stability up to a shift function.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
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.
