2 x 2 hyperbolic systems of conservation laws in classes of functions of bounded p-variation

Olivier Glass

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arXiv · 2405.02123

2 x 2 hyperbolic systems of conservation laws in classes of functions of bounded p-variation

Olivier Glass

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Abstract

In this paper, we consider $2 \times 2$ hyperbolic systems of conservation laws in one space dimension with characteristic fields satisfying a condition that encompasses genuine nonlinearity and linear degeneracy as well as intermediate cases, namely, with standard notations, $r_i\cdot \nabla \lambda_i \geq 0$. We prove the existence of entropy solutions in the fractional $BV$ spaces ${W}_p(\mathbb{R})$ of functions of bounded $p$-variation, $p \in [1,\frac{3}{2}]$, for small initial data.

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Olivier Glass. 2024-05-03. 2 x 2 hyperbolic systems of conservation laws in classes of functions of bounded p-variation. https://arxiv.org/abs/2405.02123

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