共查询到20条相似文献,搜索用时 46 毫秒
1.
Bahriye Karaca 《复变函数与椭圆型方程》2020,65(10):1748-1762
ABSTRACT Complex model partial differential equations of arbitrary order are considered. The uniqueness of the Dirichlet problem is studied. It is proved that the Dirichlet problem for higher order complex partial differential equations with one complex variable has infinitely many solutions. 相似文献
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The eigenvalue problem for elliptic partial differential equation with multi-point nonlocal conditions 下载免费PDF全文
Ahmed Elsai Shaimaa Helal Ahmed El-Sayed 《Journal of Applied Analysis & Computation》2015,5(1):146-158
We study the spectral problem for the system of difference equations of a two-dimensional elliptic partial differential equation with nonlocal conditions. A new form of two-point nonlocal conditions that involve interior points is proposed. The matrix of the difference system is nonsymmetric thus different types of eigenvalues occur. The conditions for the existence of the eigenvalues and their corresponding eigenvectors are presented for the one dimensional problem. Then, these relations are generalized to the two-dimensional problem by the separation of variables technique. 相似文献
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将Radon变换及其反投影变换原理应用于二维椭圆型偏微分方程反势问题的求解,从另一个角度解决了小扰动情况下椭圆型偏微分方程的反势问题. 相似文献
4.
Reproducing kernel method to solve parabolic partial differential equations with nonlocal conditions
Tofigh
Allahviranloo Hussein Sahihi 《Numerical Methods for Partial Differential Equations》2020,36(6):1758-1772
In this study, the parabolic partial differential equations with nonlocal conditions are solved. To this end, we use the reproducing kernel method (RKM) that is obtained from the combining fundamental concepts of the Galerkin method, and the complete system of reproducing kernel Hilbert space that was first introduced by Wang et al. who implemented RKM without Gram–Schmidt orthogonalization process. In this method, first the reproducing kernel spaces and their kernels such that satisfy the nonlocal conditions are constructed, and then the RKM without Gram–Schmidt orthogonalization process on the considered problem is implemented. Moreover, convergence theorem, error analysis theorems, and stability theorem are provided in detail. To show the high accuracy of the present method several numerical examples are solved. 相似文献
5.
M. E. Salukvadze M. T. Tcutcunava 《Journal of Optimization Theory and Applications》1987,52(2):311-322
An optimal control problem of the Gourse type with delay is investigated. With a given aim functional, a necessary condition of optimality is formulated and proved in the form of a maximum principle. The proof is based on the reduction of a problem with delay to a problem without delay.The authors thank Prof. G. Leitmann, University of California, Berkeley, for discussions and for his interest in this paper. 相似文献
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We propose a non-standard approach to impulsive differential equations in Banach spaces by embedding this type of problems into differential (dynamic) problems on time scales. We give an existence result for dynamic equations and, as a consequence, we obtain an existence result for impulsive differential equations. 相似文献
7.
Xicheng Zhang 《Journal of Functional Analysis》2007,249(2):454-476
In this paper, we study the regularities of solutions to semilinear stochastic partial differential equations in general settings, and prove that the solution can be smooth arbitrarily when the data is sufficiently regular. As applications, we also study several classes of semilinear stochastic partial differential equations on abstract Wiener space, complete Riemannian manifold as well as bounded domain in Euclidean space. 相似文献
8.
Numerical solution of linear and nonlinear partial differential equations using the peridynamic differential operator 下载免费PDF全文
Erdogan Madenci Mehmet Dorduncu Atila Barut Michael Futch 《Numerical Methods for Partial Differential Equations》2017,33(5):1726-1753
This study presents numerical solutions to linear and nonlinear Partial Differential Equations (PDEs) by using the peridynamic differential operator. The solution process involves neither a derivative reduction process nor a special treatment to remove a jump discontinuity or a singularity. The peridynamic discretization can be both in time and space. The accuracy and robustness of this differential operator is demonstrated by considering challenging linear, nonlinear, and coupled PDEs subjected to Dirichlet and Neumann‐type boundary conditions. Their numerical solutions are achieved using either implicit or explicit methods. © 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1726–1753, 2017 相似文献
9.
《Optimization》2012,61(12):2157-2177
10.
The generalized solution of ill-posed boundary problem 总被引:1,自引:0,他引:1
CAO Weiping & MA Jipu Department of Mathematics Physics Huaihai Institute of Technology Lianyungang China Y. Y. Tseng Functional Analysis Research Centre Harbin Normal University Harbin China 《中国科学A辑(英文版)》2006,49(7):902-911
In this paper, we define a kind of new Sobolev spaces, the relative Sobolev spaces Wk,p0(Ω,∑). Then an elliptic partial differential equation of the second order with an ill-posed boundary is discussed. By utilizing the ideal of the generalized inverse of an operator, we introduce the generalized solution of the ill-posed boundary problem. Eventually, the connection between the generalized inverse and the generalized solution is studied. In this way, the non-instability of the minimal normal least square solution of the ill-posed boundary problem is avoided. 相似文献
11.
Oscillation for systems of nonlinear neutral type parabolic partial functional differential equations 总被引:14,自引:0,他引:14
YANGJUN GUANXINPING 《高校应用数学学报(英文版)》1997,12(2):165-178
This paper discusses the oscillation of solutions for systems of nonlinear neutral type parabolic partial fuctional differential equations of the form 相似文献
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We study the Cauchy problem for a scalar semilinear degenerate parabolic partial differential equation with stochastic forcing. In particular, we are concerned with the well-posedness in any space dimension. We adapt the notion of kinetic solution which is well suited for degenerate parabolic problems and supplies a good technical framework to prove the comparison principle. The proof of existence is based on the vanishing viscosity method: the solution is obtained by a compactness argument as the limit of solutions of nondegenerate approximations. 相似文献
14.
Yuji Liu 《Journal of Mathematical Analysis and Applications》2006,323(1):721-740
The existence of solutions of the two-point boundary value problems consisting of the even-order differential equations
15.
W. R. Zimmerman 《Numerical Methods for Partial Differential Equations》1997,13(6):601-615
A general approach for solving systems of time domain partial differential equations using circuit analysis programs is described. The approach is then used to solve a nonlinear one-dimensional transient fluid flow problem. Using the general purpose circuit analysis program SPICE, the approach is fully implicit and should provide a convenient method for physical simulations in one dimension. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 601–615, 1997 相似文献
16.
Under certain conditions, solutions of the boundary value problem, y″=f(x,y,y′), y(x1)=y1, and , are differentiated with respect to boundary conditions, where a<x1<η1<?<ηm<x2<b, r1,…,rm∈R, and y1,y2∈R. 相似文献
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Jens Flemming 《Applicable analysis》2013,92(5):1029-1044
Numerical solution of ill-posed operator equations requires regularization techniques. The convergence of regularized solutions to the exact solution can be usually guaranteed, but to also obtain estimates for the speed of convergence one has to exploit some kind of smoothness of the exact solution. We consider four such smoothness concepts in a Hilbert space setting: source conditions, approximate source conditions, variational inequalities, and approximate variational inequalities. Besides some new auxiliary results on variational inequalities the equivalence of the last three concepts is shown. In addition, it turns out that the classical concept of source conditions and the modern concept of variational inequalities are connected via Fenchel duality. 相似文献
20.
We establish new Kamenev-type oscillation criteria for the half-linear partial differential equation with damping under quite general conditions. These results are extensions of the recent results developed by Sun [Y.G. Sun, New Kamenev-type oscillation criteria of second order nonlinear differential equations with damping, J. Math. Anal. Appl. 291 (2004) 341-351] for second order ordinary differential equations in a natural way, and improve some existing results in the literature. As applications, we illustrate our main results using two different types of half-linear partial differential equations. 相似文献