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RIGOROUS ESTIMATES ON balance laws IN BOUNDED DOMAINS

Acta Mathematica Scientia 2015年第4期35卷 906-944页

作者： Rinaldo M.COLOMBO Elena ROSSI Unità INdA M Università di Brescia Dipartimento di Matematica ed Applicazioni Università di Milano-Bicocca

The initial-boundary value problem for a general balance law in a bounded domain is proved to be well posed. Indeed, we show the existence of an entropy solution, its uniqueness and its Lipschitz continuity as a function of time, of the initial datum and of the boundary datum. The proof follows the general lines in [4], striving to provide a rigorous treatment and detailed references.

关键词： balance laws initial-boundary value problem for balance laws

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ASYMPTOTIC RAREFACTION WAVES FOR balance laws WITH STIFF SOURCES

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Acta Mathematica Scientia 2009年第6期29卷 1613-1628页

作者： W. Lambert D. Marchesin 1-Instituto Nacional de Matemtica Pura e Aplicada Estrada Dona Castorina 11022460-320 Rio de Janeiro RJ Brazil Instituto de Matemtica Pura e Aplicada Estrada Dona Castorina 11022460-320 Rio de Janeiro RJ Brazil

We study the long time formation of rarefaction waves appearing in balance laws by means of singular perturbation methods. The balance laws are non standard because they contain a variable u that appears only in the flux terms. We present a concrete example occurring in flow of steam, nitrogen and water in porous media and an abstract example for a class of systems of three equations. In the concrete example the zero-order equations resulting from the expansion yield a type of conservation law system called compositional model in Petroleum Engineering. In this work we show how compositional models originate from physically more fundamental systems of balance laws. Under appropriate conditions, we prove that certain solutions of the system of balance laws decay with time to rarefaction wave solutions in the compositional model originating from the system of balance laws.

关键词： balance laws asymptotic expansion rarefaction waves compositional models

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Regularity of Fluxes in Nonlinear Hyperbolic balance laws

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Communications on Applied Mathematics and Computation 2023年第3期5卷 1289-1298页

作者： Matania Ben-Artzi Jiequan Li Institute of Mathematics Hebrew University of Jerusalem91904 JerusalemIsrael Academy of Multidisciplinary Studies Capital Normal UniversityBeijing 100048China State Key Laboratory for Turbulence Research and Complex System Peking UniversityBeijing 100871China

This paper addresses the issue of the formulation of weak solutions to systems of nonlinear hyperbolic conservation laws as integral balance *** basic idea is that the“meaningful objects”are the fluxes,evaluated across domain boundaries over time *** fundamental result in this treatment is the regularity of the flux trace in the multi-dimensional *** implies that a weak solution indeed satisfies the balance *** fact,it is shown that the flux is Lipschitz continuous with respect to suitable perturbations of the *** should be emphasized that the weak solutions considered here need not be entropy ***,the assumption imposed on the flux f(u)is quite minimal-just that it is locally bounded.

关键词： balance laws Hyperbolic conservation laws Multi-dimensional Discontinuous solutions Finite-volume schemes Flux Trace on boundary

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Initial and Boundary Value Problem for a System of balance laws from Chemotaxis:Global Dynamics and Diffusivity Limit

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Annals of Applied Mathematics 2021年第1期37卷 61-110页

作者： Zefu Feng Jiao Xu Ling Xue Kun Zhao School of Mathematical Sciences Chongqing Normal UniversityChongqing 400047China SUSTech International Center for Mathematics Southern University of Science and TechnologyShenzhen 518055GuangdongChina College of Mathematical Sciences Harbin Engineering UniversityHarbin 150001HeilongjiangChina Department of Mathematics Tulane UniversityNew OrleansLA 70118USA

In this paper,we study long-time dynamics and diffusion limit of large-data solutions to a system of balance laws arising from a chemotaxis model with logarithmic sensitivity and nonlinear production/degradation *** energy methods,we show that under time-dependent Dirichlet boundary conditions,long-time dynamics of solutions are driven by their boundary data,and there is no restriction on the magnitude of initial ***,the zero chemical diffusivity limit is established under zero Dirichlet boundary conditions,which has not been observed in previous studies on related models.

关键词： balance laws chemotaxis initial-boundary value problem dynamic boundary condition strong solution long-time behavior diffusivity limit

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