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In this article, we consider the Ericksen-Leslie's hyperbolic system for incompressible liquid crystal model without kinematic transport in three spatial dimensions, which is a nonlinear coupling of incompressible Navier-Stokes equations…

Analysis of PDEs · Mathematics 2021-07-05 Jiaxi Huang , Ning Jiang , Yi-Long Luo , Lifeng Zhao

In this paper we propose an existence and uniqueness theory for the solutions of a system of non-linear hyperbolic conservation laws, structured in age and maturity variables, representing a tissue environment. In particular we are…

Analysis of PDEs · Mathematics 2014-08-22 Di Bernardo Laura , Donatella Donatelli

In this paper we study higher order weakly hyperbolic equations with time dependent non-regular coefficients. The non-regularity here means less than H\"older, namely bounded coefficients. As for second order equations in \cite{GR:14} we…

Analysis of PDEs · Mathematics 2015-04-16 Claudia Garetto

This paper gives a summary of a body of work at the intersection of control theory and smooth nonlinear dynamics. The main idea is to transfer the concept of uniform hyperbolicity, central to the theory of smooth dynamical systems, to…

Optimization and Control · Mathematics 2017-01-16 Christoph Kawan

We establish local well-posedness for the hyperbolic nonlinear Schrodinger equation (HNLS) in the critical spaces. Following the approach of Killip and Visan, we derive scale-invariant Strichartz estimates for HNLS on both rational and…

Analysis of PDEs · Mathematics 2025-10-06 Engin Başakoğlu , Yuzhao Wang

This paper is devoted to confront two different approaches to the problem of dynam-ical perfect plasticity. Interpreting this model as a constrained boundary value Friedrichs' system enables one to derive admissible hyperbolic boundary…

Analysis of PDEs · Mathematics 2016-11-23 Jean-Francois Babadjian , Clément Mifsud

We obtain a system for the spatial metric and extrinsic curvature of a spacelike slice that is hyperbolic non-strict in the sense of Leray and Ohya and is equivalent to the Einstein equations. Its characteristics are the light cone and the…

General Relativity and Quantum Cosmology · Physics 2012-08-27 Andrew Abrahams , Arlen Anderson , Yvonne Choquet-Bruhat , James W. York,

A classical result in thermodynamic formalism is that for uniformly hyperbolic systems, every H\"older continuous potential has a unique equilibrium state. One proof of this fact is due to Rufus Bowen and uses the fact that such systems…

Dynamical Systems · Mathematics 2020-12-21 Vaughn Climenhaga , Daniel J. Thompson

We consider solutions of hyperbolic conservation laws regularized with vanishing diffusion and dispersion terms. Following a pioneering work by Schonbek, we establish the convergence of the regularized solutions toward discontinuous…

Analysis of PDEs · Mathematics 2007-12-04 Cezar Kondo , Philippe G. LeFloch

The aim of the paper is to study local Hadamard well-posedness for wave equation with an hyperbolic dynamical boundary condition, internal and/or boundary damping and sources for initial data in the natural energy space. Moreover the…

Analysis of PDEs · Mathematics 2020-04-13 Enzo Vitillaro

Given a strictly hyperbolic $n\times n$ system of conservation laws, it is well known that there exists a unique Lipschitz semigroup of weak solutions, defined on a domain of functions with small total variation, which are limits of…

Analysis of PDEs · Mathematics 2023-05-30 Alberto Bressan , Camillo De Lellis

By a semi-Lagrangian change of coordinates, the hydrostatic Euler equations describing free-surface sheared flows is rewritten as a system of quasilinear equations, where stability conditions can be determined by the analysis of its…

We provide several characterizations of convergence to unstable equilibria in nonlinear systems. Our current contribution is three-fold. First we present simple algebraic conditions for establishing local convergence of non-trivial…

Dynamical Systems · Mathematics 2016-11-17 A. N. Gorban , I. Yu. Tyukin , H. Nijmeijer

In this work, we introduce a novel approach to formulating an artificial viscosity for shock capturing in nonlinear hyperbolic systems by utilizing the property that the solutions of hyperbolic conservation laws are not reversible in time…

Numerical Analysis · Mathematics 2022-04-20 Tarik Dzanic , Will Trojak , Freddie D. Witherden

Classifications of symmetries and conservation laws are presented for a variety of physically and analytically interesting wave equations with power onlinearities in n spatial dimensions: a radial hyperbolic equation, a radial Schrodinger…

Mathematical Physics · Physics 2007-05-23 Stephen C. Anco , Nataliya M. Ivanova

We consider a system of two kinetic equations modelling a multicellular system : The first equation governs the dynamics of cells, whereas the second kinetic equation governs the dynamics of the chemoattractant. For this system, we first…

Analysis of PDEs · Mathematics 2019-07-30 Mohamed Khaladi , Nisrine Outada , Nicolas Vauchelet

An Euler-type hyperbolic-parabolic system of chemotactic aggregation describing the vascular network formation is investigated in the critical regularity setting. For small initial data around a constant equilibrium state, the…

Analysis of PDEs · Mathematics 2023-03-17 Timothée Crin-Barat , Qingyou He , Ling-Yun Shou

This paper deals with a nonlocal model for a hyperbolic phase field system coupling the standard energy balance equation for temperature with a dynamic for the phase variable: the latter includes an inertial term and a nonlocal…

Analysis of PDEs · Mathematics 2024-02-20 Pierluigi Colli , Shunsuke Kurima , Luca Scarpa

A general nonequilibrium thermodynamic theory is developed for time-dependent Langevin dynamics, starting from the common definition of nonequilibrium Gibbs entropy. It is shown that the notations appearing in the First and the Second Law…

Statistical Mechanics · Physics 2009-04-15 Hao Ge

This paper is devoted to the controllability of a general linear hyperbolic system in one space dimension using boundary controls on one side. Under precise and generic assumptions on the boundary conditions on the other side, we previously…

Optimization and Control · Mathematics 2019-10-29 Jean-Michel Coron , Hoai-Minh Nguyen