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991.
In this paper, we study mixed non-linear fractional delay differential equations with integral boundary conditions. We obtain an equivalence result between the proposed problem and non-linear Fredholm integral equation of the second kind. Further, we establish existence and uniqueness of positive solutions for the problem using Guo-Krasnoseleskii''s fixed point theorem and Banach contraction principle. 相似文献
992.
Gui-Qiang G.CHEN 《数学年刊B辑(英文版)》2015,36(5):715-736
This paper presents several examples of fundamental problems
involving weak continuity and compactness for nonlinear partial
differential equations, in which compensated compactness and related
ideas have played a significant role. The compactness and
convergence of vanishing viscosity solutions for nonlinear
hyperbolic conservation laws are first analyzed, including the
inviscid limit from the Navier-Stokes equations to the Euler
equations for homentropic flow, the vanishing viscosity method to
construct the global spherically symmetric solutions to the
multidimensional compressible Euler equations, and the
sonic-subsonic limit of solutions of the full Euler equations for
multi-dimensional steady compressible fluids. Then the weak
continuity and rigidity of the Gauss-Codazzi-Ricci system and
corresponding isometric embeddings in differential geometry are
revealed. Further references are also provided for some recent
developments on the weak continuity and compactness for nonlinear
partial differential equations. 相似文献
993.
Iva Franjić 《Mathematische Nachrichten》2015,288(17-18):2016-2027
This paper aims to contribute to the exploration of quadrature formulae by proving that the error of a quadrature formula has the Schur‐convexity property. The emphasis is on the quadrature formulae with the maximum degree of precision. The Schur‐convexity of the error has an interesting implication – the monotonicity of the error. Namely, it turns out that the absolute value of the error is always smaller on a smaller interval (of the two which share the same midpoint). 相似文献
994.
We concern the inverse problem of determination of unknown source term for one-dimensional hyperbolic half-linear equation. Approach form for inverse problem is given by using correlative problem of assistant. We concern more ordinary problem than this paper, which is turned into integral equation with the method of characteristic line. We prove the existence and uniqueness of part solution for inverse problem, and unknown source can be solved bv successive approximation. 相似文献
995.
996.
Mustafa Gülsu Mehmet Sezer 《Numerical Methods for Partial Differential Equations》2011,27(6):1628-1638
A numerical method based on the Taylor polynomials is introduced in this article for the approximate solution of the pantograph equations with constant and variable coefficients. Some numerical examples, which consist of the initial conditions, are given to show the properties of the method. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27:1628–1638, 2011 相似文献
997.
L. Gemignani 《Applied mathematics and computation》2011,217(19):7573-7578
Diagonal plus semiseparable matrices are constructed, the eigenvalues of which are algebraic numbers expressed by simple closed trigonometric formulas. 相似文献
998.
The subject of this paper is to study the problem of the approximation of function of two variables by means of Chlodowsky-Taylor polynomials in a rectangular domain. 相似文献
999.
Increasing competition in the process industries enforces theapplication of mathematical simulation techniques both in thedesign phase and in the operating phase of a plant. A basicapparatus for separation processes is the distillation column.Its rigorous (tray by tray) mathematical modelling results ina system of simultaneous nonlinear equations (algebraic in thesteady-state case, differential-algebraic in the dynamic case).For high (and realistic) numbers of trays and components, thesesystems may become rather large (thousands of equations). Inaddition, realistic plant models often include several distillationcolumns. As a consequence, the numerical solution of these modelsmay become difficult and time-consuming. This has led to attemptsto model the distillation columns less rigorously with the aimof achieving a considerable reduction in the number of equations.The name shortcut distillation columns is common for modelsof this type. The present paper uses a discrete weighted residualmethod for the development of short-cut models. It suggestsa Galerkin method based on orthogonal polynomials in a discretevariable: the tray number. It is a remarkable advantage of thistechnique that even very coarse models satisfy all global balancesexactly. 相似文献
1000.
The Goursat formula for the hypergeometric function extends the Euler–Gauss relation to the case of logarithmic singularities. 相似文献