共查询到20条相似文献,搜索用时 78 毫秒
1.
Marius Buliga 《Journal of Elasticity》1998,52(3):201-238
2.
Boris Haspot 《Journal of Mathematical Fluid Mechanics》2011,13(2):223-249
This work is devoted to proving existence of global weak solutions for a general isothermal model of capillary fluids derived
by Dunn and Serrin (Arch Rational Mech Anal 88(2):95–133, 1985) which can be used as a phase transition model. We improve
the results of Danchin and Desjardins (Annales de l’IHP, Analyse non linéaire 18:97–133, 2001) by showing the existence of
global weak solution in dimension two for initial data in the energy space, close to a stable equilibrium and with specific
choices on the capillary coefficients. In particular we are interested in capillary coefficients approximating a constant
capillarity coefficient κ. To finish we show the existence of global weak solution in dimension one for a specific type of capillary coefficients with
large initial data in the energy space. 相似文献
3.
Eduard Feireisl 《Archive for Rational Mechanics and Analysis》2003,167(4):281-308
We prove the existence of global-in-time weak solutions to a model describing the motion of several rigid bodies in a viscous
compressible fluid. Unlike most recent results of similar type, there is no restriction on the existence time, regardless
of possible collisions of two or more rigid bodies and/or a contact of the bodies with the boundary.
(Accepted September 23, 2002)
Published online February 4, 2003
Communicated by Y. Brenier 相似文献
4.
We investigate the existence of traveling wave solutions for a system of reaction–diffusion equations that has been used as a model for microbial growth in a flow reactor and for the diffusive epidemic population. The existence of traveling waves was conjectured early but only has been proved recently for sufficiently small diffusion coefficient by the singular perturbation technique. In this paper we show the existence of traveling waves for an arbitrary diffusion coefficient. Our approach is a shooting method with the aid of an appropriately constructed Liapunov function.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthday.Wenzhang Huang-Research was supported in part by NSF Grant DMS-0204676. 相似文献
5.
We address a finite-plasticity model based on the symmetric tensor \(\varvec{P}^\top \! \varvec{P}\) instead of the classical plastic strain \(\varvec{P}\). Such a structure arises by assuming that the material behavior is invariant with respect to frame transformations of the intermediate configuration. The resulting variational model is lower dimensional, symmetric and based solely on the reference configuration. We discuss the existence of energetic solutions at the material-point level as well as the convergence of time discretizations. The linearization of the model for small deformations is ascertained via a rigorous evolution-\(\Gamma \)-convergence argument. The constitutive model is combined with the equilibrium system in Part II where we prove the existence of quasistatic evolutions and ascertain the linearization limit (Grandi and Stefanelli in 2016). 相似文献
6.
We consider a one-dimensional continuous model of nutron star, which is described by a compressible thermoviscoelastic system
with a non-monotone equation of state, due to the effective Skyrme nuclear interaction between particles. We will prove that,
despite a possible destabilizing influence of the pressure, which is non-monotone and not always positive, the presence of
viscosity and a sufficient thermal dissipation can yield the global existence of solutions in H
4 with a mixed free boundary problem for our model.
相似文献
7.
We consider the problem of designing an integral sliding mode controller for a nonlinear boost DC–DC converter based on the Takagi–Sugeno (T–S) fuzzy approach. We give an accurate T-S fuzzy model of a boost converter. We derive an existence condition of a sliding surface in terms of linear matrix inequalities (LMIs). We give a parameterization of the sliding surface using the solution matrices of the LMI existence condition. We also give a switching feedback control strategy to guarantee the reachability condition. We show that the proposed method can robustly regulate the output voltage under bounded model uncertainties. Finally, we give some simulation and experimental results to show the practicality and feasibility of the proposed method. 相似文献
8.
The present paper concerns the existence and the asymptotic stability of a stationary solution to the initial boundary value
problem for a one-dimensional heat-conductive hydrodynamic model for semiconductors. It is important to analyze thermal influence
on the motion of electrons in semiconductor device to improve the reliability of devices by handling a hot carrier problem.
We show the unique existence of the stationary solution satisfying a subsonic condition by using the Leray–Schauder and the
Schauder fixed-point theorems. Then the asymptotic stability of the stationary solution is proved by deriving the a priori
estimate uniformly in time. Here an energy form plays an essential role. We also prove that the solution converges to the
stationary solution exponentially fast as time tends to infinity. 相似文献
9.
10.
In this work, we present a new formulation for Nagdhi's model for shells with little regularity. This formulation allows for existence and uniqueness for general shells with discontinuous curvatures. We show that it coincides with the classical formulation when both are valid. We furthermore establish the continuous dependence of the solution to Nagdhi's problem on the midsurface. 相似文献
11.
D. Bresch B. Desjardins J. -M. Ghidaglia E. Grenier 《Archive for Rational Mechanics and Analysis》2010,196(2):599-629
This paper deals with mathematical properties of a generic two-fluid flow model commonly used in industrial applications.
More precisely, we address the question of whether available mathematical results in the case of a single-fluid governed by
the compressible barotropic Navier–Stokes equations may be extended to such a two-phase model. We focus on existence of global
weak solutions, linear theory and determination of eigenvalues and invariant regions. 相似文献
12.
We investigate the existence of periodic solutions for a semilinear (nonlinearly coupled) magnetoelastic system in bounded, simply connected, three-dimensional domains with boundaries of class C 2. The mathematical model includes a nonlinear mechanical dissipation like ρ(u′)=|u′| p u′ and a periodic forcing function of period T. We prove the existence of T-periodic weak solutions when p∈[3,4] (p=0 being a simpler case). In the corresponding two-dimensional case, the existence result holds under the assumption that p≥2. 相似文献
13.
David Norman 《Journal of Dynamics and Differential Equations》2000,12(2):273-307
In this paper we consider the existence and properties of strong solutions for a model of incompressible chemically reacting flows where reactants enter the domain, react, and then leave the domain. We show results which exactly parallel those of the Navier–Stokes equations, i.e., in two dimensions strong solutions exist for all time, and in three dimensions we show existence only for small times. In two dimensions, we also show the existence of global attractors which are compact in L
2. Rather than considering a specific set of boundary conditions, we instead state our results based on a series of assumptions, which would be proved using the boundary conditions. This allows our results to be applied directly to the two sets of boundary conditions which appear in the literature. 相似文献
14.
Olivier Alvarez Philippe Hoch Yann Le Bouar Régis Monneau 《Archive for Rational Mechanics and Analysis》2006,181(3):449-504
We study a mathematical model describing dislocation dynamics in crystals. We consider a single dislocation line moving in
its slip plane. The normal velocity is given by the Peach-Koehler force created by the dislocation line itself. The mathematical
model is an eikonal equation with a velocity which is a non-local quantity depending on the whole shape of the dislocation
line. We study the special case where the dislocation line is assumed to be a graph or a closed loop. In the framework of
discontinuous viscosity solutions for Hamilton–Jacobi equations, we prove the existence and uniqueness of a solution for small
time. We also give physical explanations and a formal derivation of the mathematical model. Finally, we present numerical
results based on a level-sets formulation of the problem. These results illustrate in particular the fact that there is no
general inclusion principle for this model. 相似文献
15.
We consider a dissipative model recently proposed by M. Frémond to describe the evolution of damage in elastic materials. The corresponding PDEs system consists of an elliptic equation for the displacements with a degenerating elastic coefficient coupled with a variational dissipative inclusion governing the evolution of damage. We prove a local-in-time existence and uniqueness result for an associated initial and boundary value problem, namely considering the evolution in some subinterval where the damage is not complete. The existence result is obtained by a truncation technique combined with suitable a priori estimates. Finally, we give an analogous local-in-time existence and uniqueness result for the case in which we introduce viscosity into the relation for macroscopic displacements such that the macroscopic equilibrium equation is of parabolic type.Received: 31 July 2002, Accepted: 9 August 2003, Published online: 21 November 2003Correspondence to: E. Bonetti 相似文献
16.
We define hysteresis as rate-independent memory, illustrate some of its properties, and review some scalar models of elasto-plasticity: the stop, the play, the Prandtl–Ishlinski
models. In particular we study the Prager model of linear kinematic hardening, which encompasses stops and plays. We then couple the latter model with the dynamic equation for a one-dimensional system, show existence of a weak solution, and deal with its homogenization. We also discuss the extension to tensors and to three-dimensional systems.
We then deal with ferromagnetic hysteresis. We review the classic Preisach model and a vector extension. Finally, we formulate a model of vector ferromagnetic hysteresis, couple it with the magnetostatic equations, and discuss its homogenization. The latter consists in a two-length-scale model, and corresponds to a variant of the vector Preisach model. 相似文献
17.
V. Benci P. D'Avenia D. Fortunato L. Pisani 《Archive for Rational Mechanics and Analysis》2000,154(4):297-324
In this paper we study a class of Lorentz invariant nonlinear field equations in several space dimensions. The main purpose
is to obtain soliton-like solutions. These equations were essentially proposed by C. H. Derrick in a celebrated paper in 1964 as a model for elementary particles. However, an existence theory was not developed.
The fields are characterized by a topological invariant, the charge. We prove the existence of a static solution which minimizes
the energy among the configurations with nontrivial charge.
Moreover, under some symmetry assumptions, we prove the existence of infinitely many solutions, which are constrained minima
of the energy. More precisely, for every n∈:N there exists a solution of charge n.
Accepted March 13, 2000?Published online September 12, 2000 相似文献
18.
In this article, we investigate a prey– predator model with Allee effect and state-dependent impulsive harvesting. We obtain the sufficient conditions for the existence and uniqueness of order-1 periodic solution of system (1.2) by means of the geometry theory of semicontinuous dynamic system and the method of successor function. We also obtain that system (1.2) exhibits the phenomenon of heteroclinic bifurcation about parameter $\alpha $ . The methods used in this article are novel and prove the existence of order-1 periodic solution and heteroclinic bifurcation. 相似文献
19.
Yuning Liu Takéo Takahashi Marius Tucsnak 《Journal of Mathematical Fluid Mechanics》2012,14(1):177-195
In this paper we study a mathematical model for the dynamics of vesicle membranes in a 3D incompressible viscous fluid. The
system is in the Eulerian formulation, involving the coupling of the incompressible Navier–Stokes system with a phase field
equation. This equation models the vesicle deformations under external flow fields. We prove the local in time existence and
uniqueness of strong solutions. Moreover, we show that, given T > 0, for initial data which are small (in terms of T), these solutions are defined on [0, T] (almost global existence). 相似文献
20.
We prove the global existence of solutions for a shape-memory alloys constitutive model at finite strains. The model has been
presented in Evangelista et al. (Int J Numer Methods Eng 81(6):761–785, 2010) and corresponds to a suitable finite-strain version of the celebrated Souza–Auricchio model for SMAs (Auricchio and Petrini
in Int J Numer Methods Eng 55:1255–1284, 2002; Souza et al. in J Mech A Solids 17:789–806, 1998). We reformulate the model in purely variational fashion under the form of a rate-independent process. Existence of suitably
weak (energetic) solutions to the model is obtained by passing to the limit within a constructive time-discretization procedure. 相似文献