Results 11 to 20 of about 298 (54)
A Picard‐Maclaurin theorem for initial value PDEs
Abstract and Applied Analysis, Volume 5, Issue 1, Page 47-63, 2000., 2000 In 1988, Parker and Sochacki announced a theorem which proved that the Picard iteration, properly modified, generates the Taylor series solution to any ordinary differential equation (ODE) on ℜn with a polynomial generator. In this paper, we present an analogous theorem for partial differential equations (PDEs) with polynomial generators and analytic ...
G. Edgar Parker, James S. Sochacki
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Global Solution to the Three-Dimensional Incompressible Flow of Liquid Crystals [PDF]
, 2009 The equations for the three-dimensional incompressible flow of liquid crystals are considered in a smooth bounded domain. The existence and uniqueness of the global strong solution with small initial data are established.
B. Desjardins +18 more
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Oscillatory and periodic solutions to a diffusion equation of neutral type
International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 2, Page 313-348, 1999., 1999 We examine a PDE with piecewise constant time delay. The equation is of neutral type since it contains the derivative ut at different values of the t‐argument. Furthermore, the argument deviation changes its sign within intervals of unit length, so that the given PDE is alternately of retarded and advanced type.
Joseph Wiener, William Heller
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Uniqueness and comparison principles for semilinear equations and inequalities in Carnot groups
Advances in Nonlinear Analysis, 2018 Variants of the Kato inequality are proved for distributional solutions of semilinear equations and inequalities on Carnot groups. Various applications to uniqueness, comparison of solutions and Liouville theorems are presented.
D’Ambrosio Lorenzo, Mitidieri Enzo
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Nonlinear functional integrodifferential equations in Hilbert space
International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 4, Page 847-854, 1999., 1999 Let X be a Hilbert space and let Ω ⊂ Rn be a bounded domain with smooth boundary ∂Ω. We establish the existence and norm estimation of solutions for the parabolic partial functional integro‐differential equation in X by using the fundamental solution.
J. Y. Park, S. Y. Lee, M. J. Lee
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Analytical results for 2-D non-rectilinear waveguides based on the Green's function [PDF]
, 2007 We consider the problem of wave propagation for a 2-D rectilinear optical waveguide which presents some perturbation. We construct a mathematical framework to study such a problem and prove the existence of a solution for the case of small imperfections.
Ciraolo, Giulio, Magnanini, Rolando
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Multiple solutions for a problem with resonance involving the p‐Laplacian
Abstract and Applied Analysis, Volume 3, Issue 1-2, Page 191-201, 1998., 1998 In this paper we will investigate the existence of multiple solutions for the problem where Δpu = div(|∇u|p−2∇u) is the p‐Laplacian operator, Ω⫅ℝN is a bounded domain with smooth boundary, h and g are bounded functions, N ≥ 1 and 1 < p < ∞. Using the Mountain Pass Theorem and the Ekeland Variational Principle, we will show the existence of at least ...
C. O. Alves +2 more
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Effect of Torso Non-Homogeneities in the quasi-static inverse problems arising in electrocardiology
Moroccan Journal of Pure and Applied Analysis, 2019 In the present paper, an homogeneous and non-homogeneous inverse problem constrained by the stationary problem in electrocardiology representing the heart, lungs surfaces, and torso model is investigated.
Ainseba BedrEddine +2 more
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Ultra-analytic effect of Cauchy problem for a class of kinetic equations [PDF]
, 2009 The smoothing effect of the Cauchy problem for a class of kinetic equations is studied. We firstly consider the spatially homogeneous non linear Landau equation with Maxwellian molecules and inhomogeneous linear Fokker-Planck equation to show the ultra ...
Morimoto, Yoshinori, Xu, Chao-Jiang
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Boundary value problems for the diffusion equation with piecewise continuous time delay
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 1, Page 187-195, 1997., 1996 A study is made of partial differential equations with piecewise constant arguments. Boundary value problems for three types of equations are discussed delayed; alternately of advanced and retarded type; and most importantly, an equation of neutral type (that is, including the derivative at different values of time t).
Joseph Wiener, Lokenath Debnath
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