共查询到20条相似文献,搜索用时 31 毫秒
1.
2.
Manuel Del Pino Michał Kowalczyk Juncheng Wei 《Archive for Rational Mechanics and Analysis》2008,190(1):141-187
We consider the Allen–Cahn equation in a bounded, smooth domain Ω in , under zero Neumann boundary conditions, where is a small parameter. Let Γ0 be a segment contained in Ω, connecting orthogonally the boundary. Under certain nondegeneracy and nonminimality assumptions
for Γ0, satisfied for instance by the short axis in an ellipse, we construct, for any given N ≥ 1, a solution exhibiting N transition layers whose mutual distances are and which collapse onto Γ0 as . Asymptotic location of these interfaces is governed by a Toda-type system and yields in the limit broken lines with an
angle at a common height and at main order cutting orthogonally the boundary. 相似文献
3.
Let u, p be a weak solution of the stationary Navier-Stokes equations in a bounded domain N, 5N . If u, p satisfy the additional conditions
相似文献
4.
I. A. Guerra 《Journal of Dynamics and Differential Equations》2007,19(1):243-263
Consider the problem
where Ω is a bounded convex domain in
, N > 2, with smooth boundary
. We study the asymptotic behaviour of the least energy solutions of this system as
. We show that the solution remain bounded for p large. In the limit, we find that the solution develops one or two peaks away from the boundary, and when a single peak occurs, we have a characterization of its location.This research was supported by FONDECYT 1061110 and 3040059. 相似文献
5.
Robert Jensen Changyou Wang Yifeng Yu 《Archive for Rational Mechanics and Analysis》2008,190(2):347-370
For a bounded domain and , assume that is convex and coercive, and that has no interior points. Then we establish the uniqueness of viscosity solutions to the Dirichlet problem of Aronsson’s equation:
6.
Lorenzo Brandolese 《Archive for Rational Mechanics and Analysis》2009,192(3):375-401
We study the solutions of the nonstationary incompressible Navier–Stokes equations in , of self-similar form , obtained from small and homogeneous initial data a(x). We construct an explicit asymptotic formula relating the self-similar profile U(x) of the velocity field to its corresponding initial datum a(x). 相似文献
7.
A Jordan Curve Spanned by a Complete Minimal Surface 总被引:1,自引:0,他引:1
Francisco Martín Nikolai Nadirashvili 《Archive for Rational Mechanics and Analysis》2007,184(2):285-301
In this paper we construct complete (conformal) minimal immersions
which admit continuous extensions to the closed disk,
. Moreover,
is a homeomorphism and
is a (non-rectifiable) Jordan curve with Hausdorff dimension 1.
It turns out that the set of Jordan curves
constructed by the above procedure is dense in the space of Jordan curves of
with the Hausdorff metric. 相似文献
8.
We study the dynamics and regularity of level sets in solutions of the semilinear parabolic equation
9.
Yoshikazu Giga Katsuya Inui Alex Mahalov Shin’ya Matsui Jürgen Saal 《Archive for Rational Mechanics and Analysis》2007,186(2):177-224
We prove time local existence and uniqueness of solutions to a boundary layer problem in a rotating frame around the stationary
solution called the Ekman spiral. We choose initial data in the vector-valued homogeneous Besov space for 2 < p < ∞. Here the L
p
-integrability is imposed in the normal direction, while we may have no decay in tangential components, since the Besov space
contains nondecaying functions such as almost periodic functions. A crucial ingredient is theory for vector-valued homogeneous
Besov spaces. For instance we provide and apply an operator-valued bounded H
∞-calculus for the Laplacian in for a general Banach space . 相似文献
10.
We study the limit of the hyperbolic–parabolic approximation
11.
We study the dynamics of vortices in solutions of the Gross–Pitaevsky equation in a bounded, simply connected domain with natural boundary conditions on ∂Ω. Previous rigorous results have shown that for sequences of solutions with suitable well-prepared initial data, one can determine limiting vortex trajectories, and moreover that these trajectories
satisfy the classical ODE for point vortices in an ideal incompressible fluid. We prove that the same motion law holds for
a small, but fixed , and we give estimates of the rate of convergence and the time interval for which the result remains valid. The refined
Jacobian estimates mentioned in the title relate the Jacobian J(u) of an arbitrary function to its Ginzburg–Landau energy. In the analysis of the Gross–Pitaevsky equation, they allow us to use the Jacobian to locate
vortices with great precision, and they also provide a sort of dynamic stability of the set of multi-vortex configurations. 相似文献
12.
We consider the Cauchy problem for a strictly hyperbolic, N × N quasilinear system in one-space dimension
13.
The unsteady dynamics of the Stokes flows, where
, is shown to verify the vector potential–vorticity (
) correlation
, where the field
is the pressure-gradient vector potential defined by
. This correlation is analyzed for the Stokes eigenmodes,
, subjected to no-slip boundary conditions on any two-dimensional (2D) closed contour or three-dimensional (3D) surface. It is established that an asymptotic linear relationship appears, verified in the core part of the domain, between the vector potential and vorticity,
, where
is a constant offset field, possibly zero. 相似文献
14.
Two-Phase Inertial Flow in Homogeneous Porous Media: A Theoretical Derivation of a Macroscopic Model
The purpose of this article is to derive a macroscopic model for a certain class of inertial two-phase, incompressible, Newtonian
fluid flow through homogenous porous media. Starting from the continuity and Navier–Stokes equations in each phase β and γ, the method of volume averaging is employed subjected to constraints that are explicitly provided to obtain the macroscopic
mass and momentum balance equations. These constraints are on the length- and time-scales, as well as, on some quantities
involving capillary, Weber and Reynolds numbers that define the class of two-phase flow under consideration. The resulting
macroscopic momentum equation relates the phase-averaged pressure gradient to the filtration or Darcy velocity in a coupled nonlinear form explicitly given by
15.
In this paper we study linear reaction–hyperbolic systems of the form , (i = 1, 2, ..., n) for x > 0, t > 0 coupled to a diffusion equation for p
0 = p
0(x, y, θ, t) with “near-equilibrium” initial and boundary data. This problem arises in a model of transport of neurofilaments in axons.
The matrix (k
ij
) is assumed to have a unique null vector with positive components summed to 1 and the v
j
are arbitrary velocities such that . We prove that as the solution converges to a traveling wave with velocity v and a spreading front, and that the convergence rate in the uniform norm is , for any small positive α. 相似文献
16.
Mike Cullen Wilfrid Gangbo Giovanni Pisante 《Archive for Rational Mechanics and Analysis》2007,185(2):341-363
We study the evolution of a system of n particles in . That system is a conservative system with a Hamiltonian of the form , where W
2 is the Wasserstein distance and μ is a discrete measure concentrated on the set . Typically, μ(0) is a discrete measure approximating an initial L
∞ density and can be chosen randomly. When d = 1, our results prove convergence of the discrete system to a variant of the semigeostrophic equations. We obtain that
the limiting densities are absolutely continuous with respect to the Lebesgue measure. When converges to a measure concentrated on a special d–dimensional set, we obtain the Vlasov–Monge–Ampère (VMA) system. When, d = 1 the VMA system coincides with the standard Vlasov–Poisson system. 相似文献
17.
Philippe G. Ciarlet Liliana Gratie Cristinel Mardare 《Archive for Rational Mechanics and Analysis》2008,188(3):457-473
The fundamental theorem of surface theory classically asserts that, if a field of positive-definite symmetric matrices (a
αβ
) of order two and a field of symmetric matrices (b
αβ
) of order two together satisfy the Gauss and Codazzi-Mainardi equations in a simply connected open subset ω of , then there exists an immersion such that these fields are the first and second fundamental forms of the surface , and this surface is unique up to proper isometries in . The main purpose of this paper is to identify new compatibility conditions, expressed again in terms of the functions a
αβ
and b
αβ
, that likewise lead to a similar existence and uniqueness theorem. These conditions take the form of the matrix equation
18.
Thierry Cazenave Flávio Dickstein Fred B. Weissler 《Journal of Dynamics and Differential Equations》2007,19(3):789-818
In this paper, we construct solutions u(t,x) of the heat equation on such that has nontrivial limit points in as t → ∞ for certain values of μ > 0 and β > 1/2. We also show the existence of solutions of this type for nonlinear heat equations.
相似文献
19.
20.
Anne-Laure Dalibard 《Archive for Rational Mechanics and Analysis》2009,192(1):117-164
We study the limit as ε → 0 of the entropy solutions of the equation . We prove that the sequence u
ε
two-scale converges toward a function u(t, x, y), and u is the unique solution of a limit evolution problem. The remarkable point is that the limit problem is not a scalar conservation
law, but rather a kinetic equation in which the macroscopic and microscopic variables are mixed. We also prove a strong convergence
result in . 相似文献
|