共查询到20条相似文献,搜索用时 62 毫秒
1.
Moritz Kassmann 《Comptes Rendus Mathematique》2011,349(11-12):637-640
We provide a new formulation of Harnack?s inequality for nonlocal operators. In contrast to previous versions we do not assume harmonic functions to have a sign. The version of Harnack?s inequality given here generalizes Harnack?s classical result from 1887 to nonlocal situations. As a consequence we derive Hölder regularity estimates by an extension of Moser?s method. The inequality that we propose is equivalent to Harnack?s original formulation but seems to be new even for the Laplace operator. 相似文献
2.
Luise Blank Harald Garcke Lavinia Sarbu Vanessa Styles 《Numerical Methods for Partial Differential Equations》2013,29(3):999-1030
We propose and analyze a primal‐dual active set method for discretized versions of the local and nonlocal Allen–Cahn variational inequalities. An existence result for the nonlocal variational inequality is shown in a formulation involving Lagrange multipliers for local and nonlocal constraints. Local convergence of the discrete method is shown by interpreting the approach as a semismooth Newton method. Properties of the method are discussed and several numerical simulations demonstrate its efficiency. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 相似文献
3.
Recently Frank and Seiringer have shown an isoperimetric inequality for nonlocal perimeter functionals arising from Sobolev seminorms of fractional order. This isoperimetric inequality is improved here in a quantitative form. 相似文献
4.
In this article we present the first results on domain decomposition methods for nonlocal operators. We present a nonlocal variational formulation for these operators and establish the well-posedness of associated boundary value problems, proving a nonlocal Poincaré inequality. To determine the conditioning of the discretized operator, we prove a spectral equivalence which leads to a mesh size independent upper bound for the condition number of the stiffness matrix. We then introduce a nonlocal two-domain variational formulation utilizing nonlocal transmission conditions, and prove equivalence with the single-domain formulation. A nonlocal Schur complement is introduced. We establish condition number bounds for the nonlocal stiffness and Schur complement matrices. Supporting numerical experiments demonstrating the conditioning of the nonlocal one- and two-domain problems are presented. 相似文献
5.
Bedr'Eddine Ainseba 《Journal of Mathematical Analysis and Applications》2002,275(2):562-574
We prove exact and approximate controllability for a linear age-dependent and spatially structured population dynamics problem. The birth process is nonlocal, and the demographic functions depends on age, time, and space. Our method relies on the derivation of a Carleman inequality for the backward nonlocal adjoint system. 相似文献
6.
Lower Bound Estimate of Blow Up Time for the Porous Medium Equations under Dirichlet and Neumann Boundary Conditions
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Yingzhen Xue 《偏微分方程(英文版)》2021,34(1):94-102
In this paper, we establish the lower bounds estimate of the blow up time
for solutions to the nonlocal cross-coupled porous medium equations with nonlocal
source terms under Dirichlet and Neumann boundary conditions. The results are obtained by using some differential inequality technique. 相似文献
7.
We study the existence, uniqueness and continuous dependence on initial data of the solution to a nonlocal Cahn-Hilliard equation on a bounded domain. The equation generates a gradient flow for a free energy functional with nonlocal interaction. Also we apply a nonlinear Poincaré inequality to show the existence of an absorbing set in each constant mass affine space. 相似文献
8.
Ionel Sorin Ciuperca 《Journal of Mathematical Analysis and Applications》2011,383(2):597-607
We consider the problem of a deformable surface moving over a flat plane. The surfaces are separated by a small gap filled by a lubricant fluid. The mathematical model consists of the Reynolds variational inequality with nonlocal coefficients given by an integral operator which depends on the fluid pressure. The nonlocal operator represents the deformation of the lubricated surfaces. The problem considers the vertical displacement of the elastic surface from its reference configuration. The goal of the paper is to obtain the range of these admissible displacements. We present general results for nonlocal coefficients with applications to particular problems in elasto-hydrodynamic lubrication. 相似文献
9.
Potential Analysis - We prove a boundary Harnack inequality for nonlocal elliptic operators L in non-divergence form with bounded measurable coefficients. Namely, our main result establishes that... 相似文献
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12.
Yu. A. Grishina A. A. Davydov 《Proceedings of the Steklov Institute of Mathematics》2007,256(1):80-91
The structural stability of families of orbits is proved for the simplest generic smooth dynamical inequality in the plane with bounded complement of the domain of complete controllability. Typical singularities of the boundaries of nonlocal transitivity zones for such inequalities are found. The stability of these singularities under small perturbations of the generic inequality is proved. 相似文献
13.
We state and prove a general Harnack inequality for minimizers of nonlocal, possibly degenerate, integro-differential operators, whose model is the fractional p-Laplacian. 相似文献
14.
Marius Cocou Mathieu Schryve Michel Raous 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2010,94(3):721-743
The aim of this paper is to study an interaction law coupling recoverable adhesion, friction and unilateral contact between
two viscoelastic bodies of Kelvin–Voigt type. A dynamic contact problem with adhesion and nonlocal friction is considered
and its variational formulation is written as the coupling between an implicit variational inequality and a parabolic variational
inequality describing the evolution of the intensity of adhesion. The existence and approximation of variational solutions
are analysed, based on a penalty method, some abstract results and compactness properties. Finally, some numerical examples
are presented. 相似文献
15.
By exploiting a suitable Trudinger–Moser inequality for fractional Sobolev spaces, we obtain existence and multiplicity of solutions for a class of one-dimensional nonlocal equations with fractional diffusion and nonlinearity at exponential growth. 相似文献
16.
Marius Cocou Mathieu Schryve Michel Raous 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2010,61(4):721-743
The aim of this paper is to study an interaction law coupling recoverable adhesion, friction and unilateral contact between two viscoelastic bodies of Kelvin–Voigt type. A dynamic contact problem with adhesion and nonlocal friction is considered and its variational formulation is written as the coupling between an implicit variational inequality and a parabolic variational inequality describing the evolution of the intensity of adhesion. The existence and approximation of variational solutions are analysed, based on a penalty method, some abstract results and compactness properties. Finally, some numerical examples are presented. 相似文献
17.
In this article, we provide a variational theory for nonlocal problems where nonlocality arises due to the interaction in a given horizon. With this theory, we prove well-posedness results for the weak formulation of nonlocal boundary value problems with Dirichlet, Neumann, and mixed boundary conditions for a class of kernel functions. The motivating application for nonlocal boundary value problems is the scalar stationary peridynamics equation of motion. The well-posedness results support practical kernel functions used in the peridynamics setting. We also prove a spectral equivalence estimate which leads to a mesh size independent upper bound for the condition number of an underlying discretized operator. This is a fundamental conditioning result that would guide preconditioner construction for nonlocal problems. The estimate is a consequence of a nonlocal Poincaré-type inequality that reveals a horizon size quantification. We provide an example that establishes the sharpness of the upper bound in the spectral equivalence. 相似文献
18.
主要讨论了一类非线性快慢系统非局部问题的摄动解,在适当的条件下,根据不同边界层利用伸长变量和幂级数展开理论,构造了问题的形式渐近解,并利用微分不等式理论在整个区间上证明了形式渐近解的一致有效性,把奇摄动问题的摄动解推广到快慢系统非局部问题的摄动解. 相似文献
19.
We consider initial-boundary value problems for a class of singularly perturbed nonlinear integro-differential equations.
In applications, they are referred to as nonlocal reactionadvection-diffusion equations, and their solutions have moving interior
transition layers (fronts). We construct the asymptotics of such solutions with respect to a small parameter and estimate
the accuracy of the asymptotics. To justify the asymptotics, we use the asymptotic differential inequality method. 相似文献
20.
Anders Frankild 《代数通讯》2013,41(2):461-500
In this article we present a systematic study of the reflexivity properties of homologically finite complexes with respect to semidualizing complexes in the setting of nonlocal rings. One primary focus is the descent of these properties over ring homomorphisms of finite flat dimension, presented in terms of inequalities between generalized G-dimensions. Most of these results are new even when the ring homomorphism is local. The main tool for these analyses is a nonlocal version of the amplitude inequality of Iversen, Foxby, and Iyengar. We provide numerous examples demonstrating the need for certain hypotheses and the strictness of many inequalities. 相似文献