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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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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Nonanalytic-hypoellipticity for some degenerate elliptic operators
, 1972 35J70; 35A05.
M. S. Baouendi, C. Goulaouic
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A vanishing diffusion limit in a nonstandard system of phase field equations [PDF]
, 2012 We are concerned with a nonstandard phase field model of Cahn-Hilliard type. The model, which was introduced by Podio-Guidugli (Ric. Mat. 2006), describes two-species phase segregation and consists of a system of two highly nonlinearly coupled PDEs.
Colli, Pierluigi +3 more
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Asymptotic behaviour of reversible chemical reaction-diffusion equations [PDF]
, 2010 We investigate the asymptotic behavior of the a large class of reversible chemical reaction-diffusion equations with the same diffusion. In particular we prove the optimal rate in two cases : when there is no diffusion and in the classical "two-by-two ...
Gentil, Ivan, Zegarlinski, Boguslaw
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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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Eigenelements of a General Aggregation-Fragmentation Model [PDF]
, 2009 We consider a linear integro-differential equation which arises to describe both aggregation-fragmentation processes and cell division. We prove the existence of a solution $(\lb,\U,\phi)$ to the related eigenproblem.
Adimy M. +8 more
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On the global well-posedness of discrete Boltzmann systems with chemical reaction [PDF]
, 2005 Classificação AMS: 76P05, 35A05, 35L50We study an initial-boundary value problem in one-space dimension for the discrete Boltzmann equation extended to a diatomic gas undergoing both elastic multiple collisions and chemical reactions.
Bellomo +16 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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Global well-posedness for the Gross-Pitaevskii equation with an angular momentum rotational term
, 2008 In this paper, we establish the global well-posedness of the Cauchy problem for the Gross-Pitaevskii equation with an rotational angular momentum term in the space $\Real^2$.Comment: 10 ...
Avron +16 more
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