On the convergence of quasilinear viscous approximations using compensated compactness and Kinetic Formulation

Ramesh Mondal

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arXiv · 2209.01662

On the convergence of quasilinear viscous approximations using compensated compactness and Kinetic Formulation

Ramesh Mondal

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Abstract

We use the method of Compensated Compactness and Kinteic Formulation to show that the almost everywhere limit of quasilinear viscous approximations is the unique entropy solution (in the sense of {\it F. Otto}) of the corresponding scalar conservation laws on a bounded domain in $\mathbb{R}^{d}$, where the viscous term is of the form $\varepsilon\,div\left(B(u^{\varepsilon})\nabla u^{\varepsilon}\right)$.

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Ramesh Mondal. 2022-09-04. On the convergence of quasilinear viscous approximations using compensated compactness and Kinetic Formulation. https://arxiv.org/abs/2209.01662

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