Exact solution to a class of functional difference equations with application to a moving contact line flow [PDF]
, 1994 A new integral representation for the Barnes double gamma function is derived. This is canonical in the sense that solutions to a class of functional difference equations of first order with trigonometrical coefficients can be expressed in terms of the ...
Lawrie, JB, King, AC
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High-Order Integral Equation Methods for Diffraction Problems Involving Screens and Apertures [PDF]
, 2012 This thesis presents a novel approach for the numerical solution of problems of diffraction by infinitely thin screens and apertures. The new methodology relies on combination of weighted versions of the classical operators associated with the Dirichlet ...
Lintner, Stéphane Karl
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Asymptotics of a Class of Solutions to the Cylindrical Toda Equations [PDF]
, 1997 The small t asymptotics of a class of solutions to the 2D cylindrical Toda equations is computed. The solutions, q_k(t), have the representation q_k(t) = log det(I-lambda K_k) - log det(I-lambda K_{k-1}) where K_k are integral operators.
Widom, H., Tracy, C. A.
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Pseudo-differential equations, and the Bethe ansatz for the classical Lie algebras [PDF]
, 2007 The correspondence between ordinary differential equations and Bethe ansatz equations for integrable lattice models in their continuum limits is generalised to vertex models related to classical simple Lie algebras.
Dunning, Clare +4 more
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Finite element approximation of Maxwell’s equations with Debye memory [PDF]
, 2010 Copyright © 2010 Simon Shaw. All rights reserved.This article has been made available through the Brunel Open Access Publishing Fund.Maxwell’s equations in a bounded Debye medium are formulated in terms of the standard partial differential equations of ...
Simon Shaw, Shaw, S
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Asymptotically typed solutions to a semilinear integral equation [PDF]
Journal of Integral Equations and Applications, 2014 In this paper, we investigate the existence of $\mu$-pseudo almost automorphic solutions to the semilinear integral equation $x(t)=\int_{-\infty}^{t}a(t-s)[Ax(s)+f(s,x(s))]\,ds$, $t\in\mathbf{R}$ in a Banach space $\mathbf{X}$, where $a\in L^{1}(\mathbf{R}_{+})$, $A$ is the generator of an integral resolvent family of linear bounded operators defined ...
Chang, Yong-Kui +2 more
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Existence and stability of multiple spot solutions for the Gray-Scott model in R^2$ [PDF]
, 2003 Existence and Stability of Multiple Spot Solutions for the Gray-Scott Model in $R^2$ In this paper, we rigorously prove the existence and stability of multiple spot patterns for the Gray-Scott system in a two dimensional domain which are far from ...
Wei, J
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On the adjoint of a symmetric operator [PDF]
, 2007 In general it is a non-trivial task to determine the adjoint S* of an unbounded symmetric operator S in a Hilbert or Krein space. We propose a method to specify S* explicitly which makes use of two boundary mappings that satisfy an abstract Green's ...
Meda S. +47 more
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EXISTENCE AND ASYMPTOTIC STABILITY OF SOLUTIONS TO A FUNCTIONAL-INTEGRAL EQUATION
Taiwanese Journal of Mathematics, 2007 Using a fixed point theorem of Darbo type in the space of bounded continuous functions, the existence of a bounded solution of the equation \[ x(t)=f(t,x(t))+g(t,x(t))\int_{0}^{t}u(t,s,x(s))\,ds \] is obtained when \(| u(t,s,x)|\leq a(t)b(s)\) with small \(a,b\) and \(f(t,\cdot)\) and \(g(t,\cdot)\) are contractions with small constants \(k\) and \(m(t)
Liu, Zeqing, Kang, Shin Min
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An hp-version discontinuous Galerkin method for integro-differential equations of parabolic type [PDF]
, 2011 We study the numerical solution of a class of parabolic integro-differential equations with weakly singular kernels. We use an $hp$-version discontinuous Galerkin (DG) method for the discretization in time.
H. Mustapha +7 more
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