共查询到20条相似文献,搜索用时 31 毫秒
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Eduardo Hernández Jair Silvério dos Santos Katia A.G. Azevedo 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(7):2624-2634
We discuss the existence of mild, classical and strict solutions for a class of abstract differential equations with nonlocal conditions. Our technical approach allows the study of partial differential equations with nonlocal conditions involving partial derivatives or nonlinear expressions of the solution. Some concrete applications to partial differential equations are considered. 相似文献
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For backward stochastic Volterra integral equations (BSVIEs, for short), under some mild conditions, the so-called adapted solutions or adapted M-solutions uniquely exist. However, satisfactory regularity of the solutions is difficult to obtain in general. Inspired by the decoupling idea of forward–backward stochastic differential equations, in this paper, for a class of BSVIEs, a representation of adapted M-solutions is established by means of the so-called representation partial differential equations and (forward) stochastic differential equations. Well-posedness of the representation partial differential equations are also proved in certain sense. 相似文献
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In many applications, partial differential equations depend on parameters which are only approximately known. Using tools from functional analysis and global optimization, methods are presented for obtaining certificates for rigorous and realistic error bounds on the solution of linear elliptic partial differential equations in arbitrary domains, either in an energy norm, or of key functionals of the solutions, given an approximate solution. Uncertainty in the parameters specifying the partial differential equations can be taken into account, either in a worst case setting, or given limited probabilistic information in terms of clouds. 相似文献
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Keshlan S. Govinder Barbara Abraham-Shrauner 《Nonlinear Analysis: Real World Applications》2009,10(6):3381-DECMA
Hidden symmetries of differential equations are point symmetries that arise unexpectedly in the increase (equivalently decrease) of order, in the case of ordinary differential equations, and variables, in the case of partial differential equations. The origins of Type II hidden symmetries (obtained via reduction) for ordinary differential equations are understood to be either contact or nonlocal symmetries of the original equation while the origin for Type I hidden symmetries (obtained via increase of order) is understood to be nonlocal symmetries of the original equation. Thus far, it has been shown that the origin of hidden symmetries for partial differential equations is point symmetries of another partial differential equation of the same order as the original equation. Here we show that hidden symmetries can arise from contact and nonlocal/potential symmetries of the original equation, similar to the situation for ordinary differential equations. 相似文献
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Frobenius integrable decompositions are presented for a kind of ninth-order partial differential equations of specific polynomial type. Two classes of such partial differential equations possessing Frobenius integrable decompositions are connected with two rational Bäcklund transformations of dependent variables. The presented partial differential equations are of constant coefficients, and the corresponding Frobenius integrable ordinary differential equations possess higher-order nonlinearity. The proposed method can be also easily extended to the study of partial differential equations with variable coefficients. 相似文献
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In this survey, results on the existence, growth, uniqueness, and value distribution of meromorphic (or entire) solutions of linear partial differential equations of the second order with polynomial coefficients that are similar or different from that of meromorphic solutions of linear ordinary differential equations have been obtained. We have characterized those entire solutions of a special partial differential equation that relate to Jacobian polynomials. We prove a uniqueness theorem of meromorphic functions of several complex variables sharing three values taking into account multiplicity such that one of the meromorphic functions satisfies a nonlinear partial differential equations of the first order with meromorphic coefficients, which extends the Brosch??s uniqueness theorem related to meromorphic solutions of nonlinear ordinary differential equations of the first order. 相似文献
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Hang Xu Shi-Jun Liao Xiang-Cheng You 《Communications in Nonlinear Science & Numerical Simulation》2009,14(4):1152-1156
In this paper, the time fractional partial differential equations are investigated by means of the homotopy analysis method. This technique is extended to study the partial differential equations of fractal order for the first time. The accurate series solutions are obtained. This indicates the validity and great potential of the homotopy analysis method for solving nonlinear fractional partial differential equations. 相似文献
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S. G. Lobanov 《Mathematical Notes》2008,83(5-6):643-651
We justify a method for reducing a wide class of nonlinear equations (including several partial differential equations) to ordinary differential equations in locally convex spaces. The possibilities of this method are demonstrated by an example of a class of nonlinear hyperbolic partial differential equations. 相似文献
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Youssef Z. Boutros Mina B. Abd-el-Malek Nagwa A. Badran Hossam S. Hassan 《Applied Mathematical Modelling》2007
The non-linear equations of motion describing the laminar, isothermal and incompressible flow in a rectangular domain bounded by two weakly permeable, moving porous walls, which enable the fluid to enter or exit during successive expansions or contractions, are considered. We apply Lie-group method for determining symmetry reductions of partial differential equations. Lie-group method starts out with a general infinitesimal group of transformations under which given partial differential equations are invariant, then, the determining equations are derived. The determining equations are a set of linear differential equations, the solution of which gives the infinitesimals of the dependent and independent variables. After the group has been determined, a solution to the given partial differential equation may be found from the invariant surface condition such that its solution leads to similarity variables that reduce the number of independent variables in the system. Effect of the permeation Reynolds number Re and the dimensionless wall dilation rate α on self-axial velocity have been studied both analytically and numerically and the results are plotted. 相似文献
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Invariant solutions of partial differential equations are found by solving a reduced system involving one independent variable
less. When the solutions are invariant with respect to the so-called projective group, the reduced system is simply the steady
version of the original system. This feature enables us to generate unsteady solutions when steady solutions are known. The
knowledge of an optimal system of subalgebras of the principal Lie algebra admitted by a system of differential equations
provides a method of classifying H-invariant solutions as well as constructing systematically some transformations (essentially different transformations) mapping the given system to a suitable form. Here the transformations allowing to reduce the steady two-dimensional Euler
equations of gas dynamics to an equivalent autonomous form are classified by means of the program SymboLie, after that an optimal system of two-dimensional subalgebras of the principal Lie algebra has been calculated. Some steady solutions of two-dimensional Euler
equations are determined, and used to build unsteady solutions. 相似文献
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This paper is concerned with entire and meromorphic solutions of linear partial differential equations of second order with polynomial coefficients. We will characterize entire solutions for a class of partial differential equations associated with the Jacobi differential equations, and give a uniqueness theorem for their meromorphic solutions in the sense of the value distribution theory, which also applies to general linear partial differential equations of second order. The results are complemented by various examples for completeness. 相似文献
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V. D. Rushai 《Numerische Mathematik》2009,112(1):153-167
A numerical method of solution of some partial differential equations is presented. The method is based on representation of Green functions of the equations in the form of functional integrals and subsequent approximate calculation of the integrals with the help of a deterministic approach. In this case the solution of the equations is reduced to evaluation of usual (Riemann) integrals of relatively low multiplicity. A procedure allowing one to increase accuracy of the solutions is suggested. The features of the method are investigated on examples of numerical solution of the Schrödinger equation and related diffusion equation. 相似文献
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Ruth F. Curtain 《Journal of Mathematical Analysis and Applications》1977,60(3):570-595
Existence and uniqueness theorems are proved for a general class of stochastic linear abstract evolution equations, with a general type of stochastic forcing term. The abstract evolution equation is modeled using an evolution operator (or 2-parameter semigroup) approach and this includes linear partial differential equations and linear differential delay equations. The stochastic forcing term is modeled by defining an Itô stochastic integral with respect to a Hilbert space-valued orthogonal increments process, which can be used to model both Gaussian and non-Gaussian white noise processes. The theory is illustrated by examples of stochastic partial differential equations and delay equations, which arise in filtering problems for distributed and delay systems. 相似文献
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Sergio E. Serrano T. E. Unny 《Numerical Methods for Partial Differential Equations》1986,2(4):237-258
An innovative approach to the approximate solution of stochastic partial differential equations in groundwater flow is presented. The method uses a formulation of the Ito's lemma in Hilbert spaces to derive partial differential equations satisfying the moments of the solution process. Since the moments equations are deterministic, they could be solved by any analytical or numerical method existing in the literature. This permits the analysis and solution of stochastic partial differential equations occurring in two-dimensional or three-dimensional domains of any geometrical shape. The method is tested for the first time in the present paper through a practical application in a sandy phreatic aquifer at the Chalk River Nuclear Laboratories, Ontario, Canada. The equation solved is the two-dimensional LaPlace equation with a dynamic, randomly perturbed, free surface boundary condition. The moments equations are derived and solved by using the boundary integral equation method. A comparison is made with a previous analytical solution obtained by applying the randomly forced one-dimensional Boussinesq equation, and some observations on modeling procedures are given. 相似文献
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Stochastic partial differential equations of divergence form are considered in C1 domains. Existence and uniqueness results are given in a Sobolev space with weights allowing the derivatives of the solutions to blow up near the boundary.Mathematics Subject Classification (2000): 60H15, 35R60 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2011,16(6):2421-2437
Using the solutions of an auxiliary differential equation, a direct algebraic method is described to construct several kinds of exact travelling wave solutions for some Wick-type nonlinear partial differential equations. By this method some physically important nonlinear equations are investigated and new exact travelling wave solutions are explicitly obtained. In addition, the links between Wick-type partial differential equations and variable coefficient partial differential equations are also clarified generally. 相似文献