共查询到20条相似文献,搜索用时 15 毫秒
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Juan Luis Vázquez 《Journal of Mathematical Analysis and Applications》2009,354(2):674-2161
This paper deals with the Laplace equation in a bounded regular domain Ω of RN (N?2) coupled with a dynamical boundary condition of reactive-diffusive type. In particular we study the problem
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《Mathematical and Computer Modelling》1997,25(10):29-45
This paper presents a new mathematical technique called the autocontrol image-recharge method for deriving highly accurate, computationally efficient, analytical solutions to the two-dimensional Finite Domain Laplacian Equation involving coexistent Neumann and Dirichlet boundary conditions (e.g., with both transmission and reflection) and for very irregular boundary shapes. This technique is an extension of recent work presented by Li et al. [1]and is based on developing an Expansion Coefficient Recurrence Relationship for two constant sequences for the coexistent boundary conditions. 相似文献
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On a nonlocal problem for the Laplace equation in the unit ball with fractional boundary conditions 下载免费PDF全文
Mokhtar Kirane Berikbol T. Torebek 《Mathematical Methods in the Applied Sciences》2016,39(5):1121-1128
In this paper, we investigate the correct solvability for the Laplace equation with a nonlocal boundary condition in the unit ball. The considered boundary operator is of fractional order. This problem is a generalization of the well‐known Bitsadze–Samarskii problem. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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Junichi Harada 《Calculus of Variations and Partial Differential Equations》2014,50(1-2):399-435
We consider positive solutions of $\varDelta u=0$ in $\mathbf{R}_+^n$ , $\partial _{\nu }u=u^q$ on $\partial \mathbf{R}_+^n$ , where $n\ge 3$ and $q>n/(n-2)$ . We investigate the qualitative property of positive $x_n$ -axial symmetric solutions. In particular, we are concerned with the asymptotic expansion and the intersection property of positive $x_n$ -axial symmetric solutions. 相似文献
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On an integral representation of the solution of the Laplace equation with mixed boundary conditions
T. E. Moiseev 《Differential Equations》2011,47(10):1461-1467
We obtain an integral representation of the solution of the Laplace equation with three distinct boundary conditions. Depending on the statement of the problem, the homogeneous boundary value problem may have nontrivial solutions; in other cases, the solution of the homogeneous problem is zero. Note that the inhomogeneous problem is always solvable. 相似文献
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Based on an integral equation formulation, we present numerical methods for the inverse problem of recovering part of the domain boundary from boundary measurements of solutions to the Laplace equation on an accessible part of the boundary. 相似文献
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S. Ya. Yakubov 《Semigroup Forum》1996,53(1):298-316
In this paper we find conditions that guarantee that irregular boundary value problems for elliptic differential-operator
equations of the second order in an interval are coercive with a defect and fredholm; compactness of a resolvent and estimations
by spectral parameter; completeness of root functions. We apply this result to find some algebraic conditions that guarantee
that irregular boundary value problems for elliptic partial differential equations of the second order in cylindrical domains
have the same properties. Apparently this is the first paper where the regularity of an elliptic boundary value problem is
not satisfied on a manifold of the dimension equal to the dimension of the boundary. Nevertheless, the problem is fredholm
and the resolvent is compact. It is interesting to note that the considered boundary value problems for elliptic equations
in a cylinder being with separating variables are noncoercive.
I wish to thank the referee whose comments helped me improve the style of the paper. Supported in part by the Israel Ministry
of Science and Technology and the Israel-France Rashi Foundation. 相似文献
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F. Talay Akyildiz K. Vajravelu Robert A. Van Gorder 《Applied mathematics and computation》2010,216(1):221-226
The problem of the Swift-Hohenberg equation is considered in this paper. Using homotopy analysis method (HAM) the series solution is developed and its convergence is discussed and documented here for the first time. In particular, we focus on the roles of the eigenvalue parameter α and the length parameter l on the large time behaviour of the solution. For a given time t, we obtain analytical expressions for eigenvalue parameter α and length l which show how different values of these parameters may lead to qualitatively different large time profiles. Also, the results are presented graphically. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress. 相似文献
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In this paper, we consider an initial‐boundary value problem for a parabolic equation with nonlinear boundary conditions. The solution to the problem can be expressed as a convolution integral of a Green's function and two unknown functions. We change the problem to a system of two nonlinear Volterra integral equations of convolution type. By using an explicit procedure on the basis of Sinc‐function properties, the resulting integral equations are replaced by a system of nonlinear algebraic equations, whose solution yields an accurate approximate solution to the parabolic problem. Some examples are considered to illustrate the ability of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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Yuri Bakhtin 《Proceedings of the American Mathematical Society》2007,135(7):2257-2262
We prove an existence and uniqueness theorem for stationary solutions of the inviscid Burgers equation on a segment with random boundary conditions. We also prove exponential convergence to the stationary distribution.
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We consider the Laplace equation in ? d?1 × ?+ × (0,+∞) with a dynamical nonlinear boundary condition of order between 1 and 2. Namely, the boundary condition is a fractional differential inequality involving derivatives of noninteger order as well as a nonlinear source. Nonexistence results and necessary conditions are established for local and global existence. In particular, we show that the critical exponent depends only on the fractional derivative of the least order. 相似文献
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Ludmila S. Pulkina 《Proceedings of the Steklov Institute of Mathematics》2012,278(1):199-207
Two problems with nonlinear boundary conditions are studied. Existence and uniqueness theorems are proved for generalized solutions to each problem. 相似文献
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Zhengzhong Zhou 《应用数学学报(英文版)》1989,5(3):279-288
This paper describes the spectral method for numerically solving Zakharov equation with periodic boundary conditions. This method is spectral method for spatial variable and difference method for time variable. We make error estimation of approximate solution and prove the convergence of spectral method. We had given the convergence rate. Also, we prove the stability of approximate method for initial values.Project supported by the Science Foundation of the Chinese Academy of Sciences. 相似文献
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Summary. During the filling stage of an injection moulding process, which consists in casting a melt polymer in order to manufacture
plastic pieces, the free interface between polymer and air has to be precisely described. We set this interface as a zero
level set of an unknown function. This function satisfies a transport equation with boundary conditions, where the velocity
field has few regularity properties.
In a first part, we obtain existence and uniqueness result for these equations, under weaker regularity assumptions than C.
Bardos [Bar70], and C. Bardos, Y. Leroux and J.C. Nedelec [BLN79] in previous articles, but stronger assumptions than R.J.
DiPerna and P.L. Lions [DL89b] who studied the case without boundary condition. We also study some regularity properties of
the interface.
A second part is devoted to an application to injection molding of melt polymer. We give a numerical experiment which shows
that our method leads to an accurate localization of interface, which is robust, since it easily handles changes of topology
of the free interface, as bubble formation or fusion of two fronts of melt polymer.
Received November 1, 1997 / Revised version received December 9, 1998 / Published online September 24, 1999 相似文献
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Juan Manfredi Arshak Petrosyan Henrik Shahgholian 《Calculus of Variations and Partial Differential Equations》2002,14(3):359-384
We consider a free boundary problem for the p-Laplacian
describing nonlinear potential flow past a convex profile K with prescribed pressure on the free stream line. The main purpose of this paper is to study the limit as of the classical solutions of the problem above, existing under certain convexity assumptions on a(x). We show, as one can expect, that the limit solves the corresponding potential flow problem for the -Laplacian
in a certain weak sense, strong enough however, to guarantee uniqueness. We show also that in the special case the limit is given by the distance function.
Received: 10 October 2000 / Accepted: 23 February 2001 / Published online: 19 October 2001 相似文献