Viscous approximation of triangular system in 1-d with nonlinear viscosity

Boris Haspot; Animesh Jana

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arXiv · 2503.04640

Viscous approximation of triangular system in 1-d with nonlinear viscosity

Boris Haspot·Animesh Jana

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Abstract

We study the vanishing viscosity limit for $2\times2$ triangular system of hyperbolic conservation laws when the viscosity coefficients are non linear. In this article, we assume that the viscosity matrix $B(u)$ is commutating with the convective part $A(u)$. We show the existence of global smooth solution to the parabolic equation satisfying uniform total variation bound in $\varepsilon$ provided that the initial data is small in $BV$. This extends the previous result of Bianchini and Bressan [Commun. Pure Appl. Anal. (2002)] which was considering the case $B(u)=I$.

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Boris Haspot, Animesh Jana. 2025-03-06. Viscous approximation of triangular system in 1-d with nonlinear viscosity. https://arxiv.org/abs/2503.04640

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