共查询到20条相似文献,搜索用时 62 毫秒
1.
Joachim Escher Philippe Laurençot Christoph Walker 《Archive for Rational Mechanics and Analysis》2014,211(2):389-417
The evolution problem for a membrane based model of an electrostatically actuated microelectromechanical system is studied. The model describes the dynamics of the membrane displacement and the electric potential. The latter is a harmonic function in an angular domain, the deformable membrane being a part of the boundary. The former solves a heat equation with a right-hand side that depends on the square of the trace of the gradient of the electric potential on the membrane. The resulting free boundary problem is shown to be well-posed locally in time. Furthermore, solutions corresponding to small voltage values exist globally in time, while global existence is shown not to hold for high voltage values. It is also proven that, for small voltage values, there is an asymptotically stable steady-state solution. Finally, the small aspect ratio limit is rigorously justified. 相似文献
2.
Antonio Russo 《Journal of Mathematical Fluid Mechanics》2009,11(3):407-414
We consider the stationary motion of a viscous incompressible fluid in a two-dimensional exterior domain; we prove that the
problem has a solution for small values of the flux of the boundary datum through the boundary. 相似文献
3.
C. Dupaix D. Hilhorst I. N. Kostin 《Journal of Dynamics and Differential Equations》1999,11(2):333-353
We consider the one-dimensional viscous Cahn–Hilliard equation with Dirichlet boundary conditions as the limit of a corresponding Dirichlet boundary value problem for the phase field model and we prove the convergence of the attractor. No assumption on the hyperbolicity of the stationary solutions is made. 相似文献
4.
Anna De Masi Errico Presutti Dimitrios Tsagkarogiannis 《Archive for Rational Mechanics and Analysis》2011,201(2):681-725
We study the one-dimensional stationary solutions of the integro-differential equation which, as proved in Giacomin and Lebowitz (J Stat Phys 87:37–61, 1997; SIAM J Appl Math 58:1707–1729, 1998), describes the limit behavior of the Kawasaki dynamics in Ising systems with Kac potentials. We construct stationary solutions
with non-zero current and prove the validity of the Fourier law in the thermodynamic limit showing that below the critical
temperature the limit equilibrium profile has a discontinuity (which defines the position of the interface) and satisfies
a stationary free boundary Stefan problem. Under-cooling and over-heating effects are also studied: we show that if metastable
values are imposed at the boundaries then the mesoscopic stationary profile is no longer monotone and therefore the Fourier
law is not satisfied. It regains its validity however in the thermodynamic limit where the limit profile is again monotone
away from the interface. 相似文献
5.
A. L. Silvestre 《Journal of Mathematical Fluid Mechanics》2002,4(4):285-326
In this paper we study the motion of a self-propelled rigid body through a Navier-Stokes fluid that fills all the three-dimensional space exterior to it. We formulate the problem and prove the existence of a weak solution that is defined globally in time, provided that the net flux across the boundary, of the prescribed boundary values for the velocity, is zero. It is these prescribed boundary values that propel the body, and the body is free to rotate during its motion. In the special case of a body which is symmetric about an axis, and propelled by symmetric boundary values, we obtain strong solutions representing translational motions in the direction of the axis. Further, we prove that for small Reynolds numbers every steady solution with such axial symmetry is attainable as the limit, as time tends to infinity, of a strong nonsteady solution which starts from rest. 相似文献
6.
A two-dimensional, stationary boundary layer modell is derived which allows the treatment of free convection and film boiling on vertical plate and horizontal cylinder under complete consideration of temperature dependent thermophysical properties. Some qualities of these boundary layer solutions are discussed by eleminating the influences of geometry. For horizontal cylinders, a correction of heat transfer for small diameters is given. 相似文献
7.
《ournal of non Newtonian Fluid Mechanics》1998,77(3):201-231
We study the transient Couette flow of an Oldroyd fluid that fills the gap between two circular cylinders when a constant torque is suddenly applied to the inner cylinder, the outer one being kept motionless. Contrarily to most former studies, the inertia of the moving boundary is not neglected. We give the exact solutions of this problem for a wide class of initial conditions and we present a rigorous asymptotic analysis for small gap devices when the initial state is stationary. The case of Grade 2 fluids is also considered and treated. We also show in some experimental tests, that the knowledge of the relaxation curve of the angular velocity of the rotor can be used to identify the parameters of the model. 相似文献
8.
Stationary boundary value problems for the Broadwell model in a half-space and in a half-infinite channel are considered.
By means of the analogy between the stationary boundary value problems for the Broadwell equations and the initial-boundary
value problem of Carleman's system, solutions are found for various situations. Uniqueness and non-uniqueness of solutions
is discussed as well. The non-uniqueness problem in the channel leads to the investigation of the initial value problem for
Carleman's equation with partly negative initial densities. Some new results for this problem are given.
Received January 20, 1996 相似文献
9.
The problem of steady free convection boundary layer over a vertical isothermal impermeable flat plate which is embedded in
a fluid-saturated porous medium with volumetric heat generation or absorption is studied in this paper using the Darcy equation
model. The case of the externally prescribed source terms S = S(x,y) is considered in this paper. It is shown that the corresponding boundary value problem depends on the sign of the plate
temperature, which implies that the source term breaks the usual upflow or downflow symmetry of the free convection problem.
Looking for similarity solutions, analytical and numerical solutions of the transformed boundary value problem are obtained
for several values of the problem parameters. It is also shown that, contrary to the widely spread opinion, the exponential
form of the internal heat generation term is not a necessary requirement of similarity reduction. 相似文献
10.
Jong-Shenq Guo Hiroshi Matano Masahiko Shimojo Chang-Hong Wu 《Archive for Rational Mechanics and Analysis》2016,219(3):1207-1272
We study a free boundary problem associated with the curvature dependent motion of planar curves in the upper half plane whose two endpoints slide along the horizontal axis with prescribed fixed contact angles. Our first main result concerns the classification of solutions; every solution falls into one of the three categories, namely, area expanding, area bounded and area shrinking types. We then study in detail the asymptotic behavior of solutions in each category. Among other things we show that solutions are asymptotically self-similar both in the area expanding and the area shrinking cases, while solutions converge to either a stationary solution or a traveling wave in the area bounded case. We also prove results on the concavity properties of solutions. One of the main tools of this paper is the intersection number principle, however in order to deal with solutions with free boundaries, we introduce what we call “the extended intersection number principle”, which turns out to be exceedingly useful in handling curves with moving endpoints. 相似文献
11.
A convection–diffusion model for the averaged flow of a viscous, incompressible magma through an elastic medium is considered. The magma flows through a dike from a magma reservoir to the Earth’s surface; only changes in dike width and velocity over large vertical length scales relative to the characteristic dike width are considered. The model emerges when nonlinear inertia terms in the momentum equation are neglected in a viscous, low-speed approximation of a magma flow model coupled to the elastic response of the rock.Stationary- and traveling-wave solutions are presented in which a Dirichlet condition is used at the magma chamber; and either a (i) free-boundary condition, (ii) Dirichlet condition, or (iii) choked-flow condition is used at the moving free or fixed-top boundary. A choked-flow boundary condition, generally used in the coupled elastic wave and magma flow model, is also used in the convection–diffusion model. The validity of this choked-flow condition is illustrated by comparing stationary flow solutions of the convection–diffusion and coupled elastic wave and magma flow model for parameter values estimated for the Tolbachik volcano region in Kamchatka, Russia. These free- and fixed-boundary solutions are subsequently explored in a conservative, local discontinuous Galerkin finite-element discretization. This method is advantageous for the accurate implementation of the choked flow and free-boundary conditions. It uses a mixed Eulerian–Lagrangian finite element with special infinite curvature basis function near the free boundary and ensures positivity of the mean aperture subject to a time-step restriction. We illustrate the model further by simulating magma flow through host rock of variable density, and magma flow that is quasi-periodic due to the growth and collapse of a lava dome. 相似文献
12.
V. B. Bekezhanova 《Journal of Applied Mechanics and Technical Physics》2001,42(3):437-444
The stationary problem of convection in liquids is considered using the model of microconvection developed by V. V. Pukhnachev. Velocity profiles for boundary conditions of different classes are constructed. The solutions of the problem under study and the classical problem based on the Oberbeck—Boussinesq model are compared. 相似文献
13.
We suggest a new method for studying finite dimensional dynamics for evolutionary differential equations. We illustrate this
method for the case of the KdV equation. As a side result we give constructive solutions of the boundary problem for the Schrodinger
equations whose potentials are solutions of stationary KdV equations and their higher generalizations. 相似文献
14.
The axisymmetric laminar boundary layer flow along the entire length of a semi-infinite stationary cylinder under an accelerated free-stream is investigated. Considering flow at reduced dimensions, the boundary layer equations are developed with the conventional no-slip boundary condition for tangential velocity and temperature replaced by a linear slip-jump boundary condition. Asymptotic series solutions are obtained for the heat transfer coefficient in terms of the Nusselt number. These solutions correspond to prescribed values of the momentum and temperature slip coefficients and the index of acceleration. Heat transfer at both small and large axial distances is determined in the form of series solutions; whereas at intermediate distances, exact and interpolated numerical solutions are obtained. Using these results, the heat transfer along the entire cylinder wall is evaluated in terms of the parameters of acceleration and slip. 相似文献
15.
K. D. Danov R. Aust F. Durst U. Lange 《International Journal of Multiphase Flow》1995,21(6):1169-1189
In order to investigate the hydrodynamic interaction between an interface and a spherical particle and its dependence on the type of interface, it is essential to compute the drag and torque exerted on the sphere in the vicinity of the interface. In this paper, the problem of all slow elementary motions (relative translation and rotation) and stationary movement of a spherical particle next to a solid, viscous or free interface is considered. For low capillary numbers and different values of surface dilatational and shear viscosities in a curvilinear co-ordinate system of revolution with bicylindrical co-ordinates in meridian planes, the problem reduces from three to two dimensions. The model equations and boundary conditions, which contain second-order derivatives of the velocities, transform to an equivalent well-defined system of second-order partial differential equations which is solved numerically for medium and small values of the dimensionless distance to the interface. Very good agreement with the asymptotic equation for a translating sphere close to a solid interface could be achieved. The numerical results reveal in all cases the strong influence of the surface viscosity on the motion of the solid sphere. For small distances from the interface, the drag and torque coefficients change significantly depending on the surface viscosity. 相似文献
16.
We consider a kinetic model for a system of two species of particles interacting through a long range repulsive potential
and a reservoir at given temperature. The model is described by a set of two coupled Vlasov–Fokker–Plank equations. The important
front solution, which represents the phase boundary, is a stationary solution on the real line with given asymptotic values
at infinity. We prove the asymptotic stability of the front for small symmetric perturbations. 相似文献
17.
Stephan Blazy Sergueï Nazarov Maria Specovius-Neugebauer 《Journal of Mathematical Fluid Mechanics》2007,9(1):1-33
In a three-dimensional domain Ω with J cylindrical outlets to infinity the problem is treated how solutions to the stationary Stokes and Navier–Stokes system with
pressure conditions at infinity can be approximated by solutions on bounded subdomains. The optimal artificial boundary conditions
turn out to have singular coefficients. Existence, uniqueness and asymptotically precise estimates for the truncation error
are proved for the linear problem and for the nonlinear problem with small data. The results include also estimates for the
so called “do-nothing” condition. 相似文献
18.
Patrick W. Dondl Kaushik Bhattacharya 《Archive for Rational Mechanics and Analysis》2010,197(2):599-617
A model for the quasistatic evolution of martensitic phase boundaries is presented. The model is essentially the gradient
flow of an energy that can contain elastic energy due to the underlying change in crystal structure in the course of the phase
transformation and surface energy penalizing the area of the phase boundary. This leads to a free boundary problem with a
nonlocal velocity that arises from a coupling to the elasticity equation. We show existence of solutions under a technical
convergence condition using an implicit time-discretization. 相似文献
19.
R. Temam 《Archive for Rational Mechanics and Analysis》1975,60(1):51-73
A free boundary value problem arising in plasma physics is reduced to a non-linear eigenvalue problem of a non-classical type. We establish the existence of solutions of the non-linear eigenvalue problem; these solutions are critical points of appropriate functionals. 相似文献
20.
The two-dimensional problem of the electrochemical dimensional machining of a metal is investigated within the framework of
the model of an ideal stationary process, which makes it possible to use the analogy with the problems of fluid flows with
free surfaces. In the problem considered the cathode (machining tool) takes the form of two parallel semi-infinite rectangular
electrodes. The blank (anode) is a half-plane whose boundary is perpendicular to the cathodes. Depending on the relationship
between the physical and geometrical parameters of the problem, on the machined part (anode) a projection symmetrical about
the center line between the cathodes may be formed. Additional mechanical machining of the part is then required. In order
to exclude such solutions, a condition is obtained for the mathematical parameters which determine the solution of the problem
in the auxiliary complex plane. General and particular limiting cases are considered. For the cases considered the calculation
results are presented in the form of plots of the shape of the part machined. 相似文献