On a hyperbolic-parabolic system arising in magnetoelasticity
نویسندگان
چکیده
The evolution of a magnetoelastic material is described by a nonlinear hyperbolic-parabolic system. We introduce a simplified but nontrivial model and prove the existence of a unique solution to the corresponding initial boundary value problem. On a hyperbolic-parabolic system arising in magnetoelasticity M. Chipot∗ I. Shafrir† V. Valente ‡ G. Vergara Caffarelli§ November 6, 2007 keywords: Magnetoelastic materials, Nonlinear hyperbolic-parabolic systems. Abstract The evolution of a magnetoelastic material is described by a nonlinear hyperbolicparabolic system. We introduce a simplified but nontrivial model and prove the existence of a unique solution to the corresponding initial boundary value problem.The evolution of a magnetoelastic material is described by a nonlinear hyperbolicparabolic system. We introduce a simplified but nontrivial model and prove the existence of a unique solution to the corresponding initial boundary value problem.
منابع مشابه
Global Existence of Solutions to a Hyperbolic-parabolic System
In this paper, we investigate the global existence of solutions to a hyperbolic-parabolic model of chemotaxis arising in the theory of reinforced random walks. To get L2-estimates of solutions, we construct a nonnegative convex entropy of the corresponding hyperbolic system. The higher energy estimates are obtained by the energy method and a priori assumptions.
متن کاملThe Exponential Stability of a Coupled Hyperbolic/parabolic System Arising in Structural Acoustics
We show here the uniform stabilization of a coupled system of hyperbolic and parabolic PDE’s which describes a particular fluid/structure interaction system. This system has the wave equation, which is satisfied on the interior of a bounded domain Ω, coupled to a “parabolic–like” beam equation holding on ∂Ω, and wherein the coupling is accomplished through velocity terms on the boundary. Our re...
متن کاملNonlinear Stability of Large Amplitude Viscous Shock Waves of a Generalized Hyperbolic{parabolic System Arising in Chemotaxis
Traveling wave (band) behavior driven by chemotaxis was observed experimentally by Adler and was modeled by Keller and Segel. For a quasilinear hyperbolic parabolic system that arises as a non-di®usive limit of the Keller Segel model with nonlinear kinetics, we establish the existence and nonlinear stability of traveling wave solutions with large amplitudes. The numerical simulations are perfor...
متن کاملMathematical Analysis of a Nonlinear Parabolic Equation Arising in the Modelling of Non-Newtonian Flows
The mathematical properties of a nonlinear parabolic equation arising in the modelling of non-newtonian flows are investigated. The peculiarity of this equation is that it may degenerate into a hyperbolic equation (in fact a linear advection equation). Depending on the initial data, at least two situations can be encountered: the equation may have a unique solution in a convenient class, or it ...
متن کاملExistence of a Unique Solution to a Nonlinear Moving-boundary Problem of Mixed Type Arising in Modeling Blood Flow
We prove the (local) existence of a unique mild solution to a nonlinear moving-boundary problem of a mixed hyperbolic-degenerate parabolic type arising in modeling blood flow through compliant (viscoelastic) arteries.
متن کامل