Existence of BV solutions for $2\times2$ hyperbolic balance laws for $L^\infty$ initial data

Fuente: arXiv
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Main Authors: Haspot, Boris, Jana, Animesh
Format: Preprint
Published: 2024
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author Haspot, Boris
Jana, Animesh
author_facet Haspot, Boris
Jana, Animesh
contents We prove the existence of BV solutions for $2\times 2$ system of hyperbolic balance laws in one space dimension. The flux is assumed to have two genuinely nonlinear characteristic fields. We consider a general force which may possibly depend on time and space variable as well. To prove the existence, we assume the initial data to be small in $L^\infty$. Furthermore, we also study qualitative behavior for entropy solutions to hyperbolic system of balance laws.
format Preprint
id arxiv_https___arxiv_org_abs_2408_00849
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Existence of BV solutions for $2\times2$ hyperbolic balance laws for $L^\infty$ initial data
Haspot, Boris
Jana, Animesh
Analysis of PDEs
We prove the existence of BV solutions for $2\times 2$ system of hyperbolic balance laws in one space dimension. The flux is assumed to have two genuinely nonlinear characteristic fields. We consider a general force which may possibly depend on time and space variable as well. To prove the existence, we assume the initial data to be small in $L^\infty$. Furthermore, we also study qualitative behavior for entropy solutions to hyperbolic system of balance laws.
title Existence of BV solutions for $2\times2$ hyperbolic balance laws for $L^\infty$ initial data
topic Analysis of PDEs
url https://arxiv.org/abs/2408.00849