首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 15 毫秒
1.
We study a boundary value problem for a fourth-order ordinary differential equation with a nonlocal boundary condition. We give a necessary and sufficient condition for a minimizer of a specially constructed functional to be a solution of the problem.  相似文献   

2.
We study subsolutions for semilinear elliptic boundary value problems in L1. We consider as well nonlinear as linear boundary conditions. The nonlinear functions may be multivated. We characterize in terms of p.d.e. the subsolutions defined by a nonlinear functional analysis argument. Applications are given to obtain existence results for semilinear elliptic boundary value problems and comparison and estimates for nonlinear parabolic boundary value problems.  相似文献   

3.
We propose some minimum principle for an energy functional in an elliptic boundary value problem that arises in constructing time-harmonic solutions to the Maxwell equations. We suggest the potentials other than the vector and scalar potentials, used in the mathematical modeling of electromagnetic fields since the operators of traditional problems are not sign definite, which complicates constructions of iterative solution methods. We consider the problem in a parallelepiped whose boundary is ideally conducting. For nonresonant frequencies we prove that the operator of the boundary value problem is positive definite, propose a minimum principle for a quadratic energy functional, and prove the existence and uniqueness of generalized solutions.  相似文献   

4.
We introduce a purely functional analytic framework for elliptic boundary value problems in a variational form. We define abstract Neumann and Dirichlet boundary conditions and a corresponding Dirichlet‐to‐Neumann operator, and develop a theory relating resolvents and spectra of these operators. We illustrate the theory by many examples including Jacobi operators, Laplacians on spaces with (non‐smooth) boundary, the Zaremba (mixed boundary conditions) problem and discrete Laplacians.  相似文献   

5.
In this paper we study functional φ-Laplacian equations with functional boundary conditions. The non-linearity belongs to a class of completely continuous operators, which includes Carathéodory ones, while the functional boundary conditions are given by compactly-fixed operators. We extend, in particular, a solvability result of C. Bereanu and J. Mawhin.  相似文献   

6.
We look for best mean-quasiconformal mappings as extremals of the functional equal to the integral of the square of the functional of the conformality distortion multiplied by a special weight. The mapping inverse to an extremal is an extremal of the same functional. We obtain necessary and sufficient conditions for the Petrovskii ellipticity of the system of Euler equations for an extremal. We prove the local unique solvability of boundary values problems for this system in the 2-dimensional case. In the general case we prove the unique solvability of boundary value problems for the system linearized at the identity mapping.  相似文献   

7.
In this paper, we prove a bifurcation phenomenon in a two-phase, singularly perturbed, free boundary problem of phase transition. We show that the uniqueness of the solution for the two-phase problem breaks down as the boundary data decreases through a threshold value. For boundary values below the threshold, there are at least three solutions, namely, the harmonic solution which is treated as a trivial solution in the absence of a free boundary, a nontrivial minimizer of the functional under consideration, and a third solution of the mountain-pass type. We classify these solutions according to the stability through evolution. The evolution with initial data near a stable solution, such as the trivial harmonic solution or a minimizer of the functional, converges to the stable solution. On the other hand, the evolution deviates away from a non-minimal solution of the free boundary problem.  相似文献   

8.
We study a nonlocal boundary value problem for a fourth-order ordinary differential equation. We give a variational statement of the problem by constructing the corresponding functional. The minimization of this functional provides a solution of the problem.  相似文献   

9.
We consider a shape optimization problem for Maxwell's equations with a strictly dissipative boundary condition. In order to characterize the shape derivative as a solution to a boundary value problem, sharp regularity of the boundary traces is critical. This Note establishes the Fréchet differentiability of a shape functional.  相似文献   

10.
We study the minimizers, in the class of convex functions, of an elliptic functional with nonhomogeneous Dirichlet boundary conditions. We prove C1 regularity of the minimizers under the assumption that the upper envelope of admissible functions is C1. This condition is optimal at least when the functional depends only on the gradient [4]. We then extend this result to a problem without boundary conditions arising in an economic model introduced by Rochet and Choné in [5].  相似文献   

11.
We study a functional equation whose unknown maps a Euclidean space into the space of probability distributions on [0,1]. We prove existence and uniqueness of its solution under suitable regularity and boundary conditions, we show that it depends continuously on the boundary datum, and we characterize solutions that are diffuse on [0,1]. A canonical solution is obtained by means of a Randomly Reinforced Urn with different reinforcement distributions having equal means. The general solution to the functional equation defines a new parametric collection of distributions on [0,1] generalizing the Beta family.  相似文献   

12.
We suggest a geometric-dynamic approach to billiards as a special kind of reversible dynamic system and establish their relation to projective transformations (involutions) in the framework of this approach. We state the direct and inverse problems for billiards and derive equations determining the solutions of these problems in general form. Some simplest billiard involutions are calculated. We establish functional relations between the involution of a billiard, the equation for its boundary, and the field of normals to the boundary. We show how the involution is related to the curvature of the billiard boundary.  相似文献   

13.
We consider extremal problems for the time-harmonic Maxwell equations with mixed boundary conditions for the electric field. Namely, the tangential component of the electric field is given on one part of the boundary, and an impedance boundary condition is posed on the other part. We prove the solvability of the original mixed boundary value problem and the extremal problem. We obtain sufficient conditions on the input data ensuring the stability of solutions of specific extremal problems under certain perturbations of both the performance functional and some functions occurring in the boundary value problem.  相似文献   

14.
This paper studies a scalar minimization problem with an integral functional of the gradient under affine boundary conditions. A new approach is proposed using a minimal and a maximal solution to the convexified problem. We prove a density result: any relaxed solution continuously depending on boundary data may be approximated uniformly by solutions of the nonconvex problem keeping continuity relative to data. We also consider solutions to the nonconvex problem having Lipschitz dependence on boundary data with the best Lipschitz constant.  相似文献   

15.
We study extremal problems of boundary control for stationary heat convection equations with Dirichlet boundary conditions on velocity and temperature. As the cost functional we choose the mean square integral deviation of the required temperature field from a given temperature field measured in some part of the flow region. The controls are functions appearing in the Dirichlet conditions on velocity and temperature. We prove the stability of solutions to these problems with respect to certain perturbations of both the quality functional and one of the known functions appearing in the original equations of the model.  相似文献   

16.
Motivated by the interesting paper [I. Karaca, Discrete third-order three-point boundary value problem, J. Comput. Appl. Math. 205 (2007) 458–468], this paper is concerned with a class of boundary value problems for second-order functional difference equations. Sufficient conditions for the existence of at least one solution of a Sturm–Liouville boundary value problem for second-order nonlinear functional difference equations are established. We allow f to be at most linear, superlinear or sublinear in obtained results.  相似文献   

17.
In this paper, we will give conditions which will guarantee the existence of positive solutions for a variety of second order boundary value problems, using the well-known Krasnoselskii fixed point theorem. We will deal with a specific differential equation meeting a specific initial condition and use a general boundary condition, involving a not necessarily linear functional. Our purpose is to pose conditions on that functional, which will guarantee that the Krasnoselskii fixed point theorem can be applied. It is important to notice that only the values of this functional on two specific functions are involved in the conditions we pose. This paper unifies the way we deal with a wide variety of boundary value problems and provides results which, to the best of our knowledge, are new.  相似文献   

18.
We consider the Stefan problem with Dirichlet boundary conditions depending on a hysteresis functional where the free boundary is involved. We show existence of a positive valueT and existence of aT-periodic solution of the problem, provided the Stefan number is sufficiently small and the hysteresis functional is described by the elementary rectangular hysteresis loop. If in addition the Preisach hysteresis operator is Lipschitz-continuous we prove that every periodic solution must be stationary. Dedicated to Professor Avner Friedman on occasion of his 60th birthday supported by Humboldt Foundation Scholarship  相似文献   

19.
We consider linear boundary-value problems for systems of functional differential equations when the number of boundary conditions is greater than the dimension of the system. We allow the boundary conditions to be fulfilled approximately. We propose an approach based on theorems whose conditions allow the verification by special reliable computing procedures.  相似文献   

20.
We study control problems for the stationary magnetohydrodynamic equations. In these problems, one has to find an unknown vector function occurring in the boundary condition for the magnetic field and the solution of the boundary value problem in question by minimizing a performance functional depending on the velocity and pressure. We derive new a priori estimates for the solutions of the original boundary value problem and the extremal problem and prove theorems on the local uniqueness and stability of solutions for specific performance functionals.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号