共查询到20条相似文献,搜索用时 31 毫秒
1.
Sasun Yakubov 《Integral Equations and Operator Theory》1999,35(4):485-506
In this paper we give, for the first time, an abstract interpretation of nonlocal boundary value problems for elliptic differential equations of the second order. We prove coerciveness and Fredholmness of nonlocal boundary value problems for the second order elliptic differential-operator equations. We apply then, in section 6, these results for investigation of nonlocal boundary value problems for the second order elliptic differential equations (one can find the references on the subject in the introduction and Chapter V in the book by A. L. Skubachevskii [27]). Abstract results obtained in this paper can be used for study of nonlocal boundary value problems for quasielliptic differential equations. 相似文献
2.
We consider a class of fractional evolution equations with nonlocal integral conditions in Banach spaces. New existence of mild solutions to such a problem are established using Schauder fixed-point theorem, diagonal argument and approximation techniques under the hypotheses that the nonlinear term is Carathéodory continuous and satisfies some weak growth condition, the nonlocal term depends on all the value of independent variable on the whole interval and satisfies some weak growth condition. This work may be viewed as an attempt to develop a general existence theory for fractional evolution equations with general nonlocal integral conditions. Finally, as a sample of application, the results are applied to a fractional parabolic partial differential equation with nonlocal integral condition. The results obtained in this paper essentially extend some existing results in this area. 相似文献
3.
This paper deals with the existence of mild solutions for a class of semilinear nonlocal impulsive evolution equations in ordered Banach spaces. The existence and uniqueness theorem of mild solution for the associated linear nonlocal impulsive evolution equation is established. With the aid of the theorem, the existence of mild solutions for nonlinear nonlocal impulsive evolution equation is obtained by using perturbation method and monotone iterative technique. The theorems proved in this paper improve and extend some related results in ordinary differential equations and partial differential equations. Moreover, we present two examples to illustrate the feasibility of our abstract results. 相似文献
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SISSON R. A.; SWIFT A.; WAKE G. C.; GRAY B. F. 《IMA Journal of Applied Mathematics》1993,50(3):285-306
In this paper the authors analyse a spatially distributed modelfor the self-heating of damp cellulosic materials. The equationfor the steady-state temperature profiles of the system hasa nonlocal dependence on the temperature in the nonlinear expressionfor the self-heating source term. Some existence, uniqueness,and multiplicity results are presented for the steady states,extending some well-known results to include the nonlocal term. 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.
《Nonlinear Analysis: Theory, Methods & Applications》2005,62(7):1251-1265
In this paper we study the existence of positive solutions to a system of second-order nonlocal boundary value problems by using fixed point index theory in a cone. Our hypotheses imposed on nonlinearities are those which characterize systems of nonlocal boundary value problems, and our boundary value conditions are expressed in terms of possibly nonlinear functions of Riemann–Stieltjes integrals, thus generalizing and unifying the boundary value conditions in the literature. Therefore our results cannot be routinely deduced from the ones for single nonlocal problem in the literature. 相似文献
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This paper investigates the nonlinear time-space fractional reaction-diffusion equations with nonlocal initial conditions. Based on the operator semigroup theory, we transform the time-space fractional reaction-diffusion equation into an abstract evolution equation. The existence and uniqueness of mild solution to the reaction-diffusion equation are obtained by solving the abstract evolution equation. Finally, we verify the Mittag-Leffler-Ulam stabilities of the nonlinear time-space fractional reaction-diffusion equations with nonlocal initial conditions. The results in this paper improve and extend some related conclusions to this topic. 相似文献
11.
《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2019,36(6):1709-1745
The main result of this paper is a nonlocal version of Harnack's inequality for a class of parabolic nonlocal equations. We additionally establish a weak Harnack inequality as well as local boundedness of solutions. None of the results require the solution to be globally positive. 相似文献
12.
按照理性力学的本构公理系统严格推导了非线性非局部热弹性体的本构方程,修正、补充和完善了以前的工作,所得的结果表明,非局部热弹性体的本构响应是与其物质空间的曲率及其高阶梯度相关联的,且存在满足零平均条件的反对称应力;文中给出了反对称应力与局部化残余的表达式,导出了热传递方向与温度降方向一致的结论,简要论述了局部化残余以及非局部能量守恒定律的客观性。 相似文献
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In this paper, we investigate local and nonlocal reductions of a discrete negative order Ablowitz–Kaup–Newell–Segur equation. By the bilinearization reduction method, we construct exact solutions in double Casoratian form to the reduced nonlocal discrete sine-Gordon equations. Then, nonlocal semidiscrete sine-Gordon equations and their solutions are obtained through the continuum limits. The dynamics of soliton solutions are analyzed and illustrated by asymptotic analysis. The research ideas and methods in this paper can be generalized to other nonlocal discrete integrable systems. 相似文献
14.
In this paper, we study a nonlocal diffusion equation with a general diffusion kernel and delayed nonlinearity, and obtain the existence, nonexistence and uniqueness of the regular traveling wave solutions for this nonlocal diffusion equation. As an application of the results, we reconsider some models arising from population dynamics, epidemiology and neural network. It is shown that there exist regular traveling wave solutions for these models, respectively. This generalized and improved some results in literatures. 相似文献
15.
Lazhar Bougoffa 《Journal of Applied Mathematics and Computing》2013,43(1-2):31-54
In this paper, we present a new approach to solve nonlocal initial-boundary value problems of linear and nonlinear hyperbolic partial differential equations of first-order subject to initial and nonlocal boundary conditions of integral type. We first transform the given nonlocal initial-boundary value problems into local initial-boundary value problems. Then we apply a modified Adomian decomposition method, which permits convenient resolution of these problems. Moreover, we prove this decomposition scheme applied to such nonlocal problems is convergent in a suitable Hilbert space, and then extend our discussion to include systems of first-order linear equations and other related nonlocal initial-boundary value problems. 相似文献
16.
Xuping Zhang Pengyu Chen Yongxiang Li 《Numerical Functional Analysis & Optimization》2013,34(14):1678-1702
AbstractThe aim of this paper is to discuss the existence of mild solutions and positive mild solutions for a general class of semilinear fractional retarded evolution equations subjected to mixed nonlocal plus local initial conditions on infinite dimensional Banach spaces. Under the situation that the nonlinear term and nonlocal function satisfy some appropriate growth conditions and a noncompactness measure condition, we obtained the existence of mild solutions and positive mild solutions by utilizing a generalized Darbo’s fixed point theorem and a new estimation technique of the measure of noncompactness. In addition, the strong restriction on the constants in the condition of noncompactness measure is completely deleted in this paper. An example about the retarded parabolic partial differential equation involving a general mixed nonlocal plus local initial conditions is also given to illustrate the feasibility of our abstract results. 相似文献
17.
Jiancai Sun 《Israel Journal of Mathematics》2016,216(1):247-272
We introduce the notion of module twistor for a module of a nonlocal vertex algebra. The aim of this paper is to use this concept to unify some deformed constructions of modules of nonlocal vertex algebras, such as twisted tensor products and iterated twisted tensor products of modules of nonlocal vertex algebras. 相似文献
18.
Buckling and free vibration analyses of nonlocal axially functionally graded Euler nanobeams is the main objective of this paper. Due to its simplicity, the Eringen's differential constitutive model is adopted for describing the nonlocal size dependency of nanostructure beam. The nonlocal equilibrium equation is derived using the principle of the minimum potential energy principle, and discretized by using the link-spring model known in literature as Hencky bar-chain model. The general applicability of the proposed approach allows analyses of functional graded microbeams without any restriction on variability, boundary and loading conditions. A comparison with results available in the literature shows the reliability of the method. 相似文献
19.
We study a nonlocal perimeter functional inspired by the Minkowski content, whose main feature is that it interpolates between the classical perimeter and the volume functional. This nonlocal functionals arise in concrete applications, since the nonlocal character of the problems and the different behaviors of the energy at different scales allow the preservation of details and irregularities of the image in the process of removing white noises, thus improving the quality of the image without losing relevant features. In this paper, we provide a series of results concerning existence, rigidity and classification of minimizers, compactness results, isoperimetric inequalities, Poincaré–Wirtinger inequalities and density estimates. Furthermore, we provide the construction of planelike minimizers for this generalized perimeter under a small and periodic volume perturbation. 相似文献
20.
In this paper, we consider a linear population dynamics model with age dependence and spatial structure in which birth process
is described by a nonlocal term. Carleman estimate for the backward nonlocal adjoint problem providing the observability results
is fundamental to the analysis and by duality it provides the controllability result. More precisely, we observe that one
can expect to compute the initial distribution using observations on a small part of the boundary. 相似文献