Displaying similar documents to “Continuity of the quenching time for a parabolic equation with a nonlinear boundary condition and a potential.”

Continuity of the quenching time in a semilinear parabolic equation

Théodore Boni, Firmin N'Gohisse (2008)

Annales UMCS, Mathematica

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In this paper, we consider the following initial-boundary value problem [...] where Ω is a bounded domain in RN with smooth boundary ∂Ω, p > 0, Δ is the Laplacian, v is the exterior normal unit vector on ∂Ω. Under some assumptions, we show that the solution of the above problem quenches in a finite time and estimate its quenching time. We also prove the continuity of the quenching time as a function of the initial data u0. Finally, we give some numerical results to illustrate our...

Convergence of a numerical scheme for a nonlinear oblique derivative boundary value problem

Florian Mehats (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We present here a discretization of a nonlinear oblique derivative boundary value problem for the heat equation in dimension two. This finite difference scheme takes advantages of the structure of the boundary condition, which can be reinterpreted as a Burgers equation in the space variables. This enables to obtain an energy estimate and to prove the convergence of the scheme. We also provide some numerical simulations of this problem and a numerical study of the stability of the scheme,...

Numerical investigation of a new class of waves in an open nonlinear heat-conducting medium

Milena Dimova, Stefka Dimova, Daniela Vasileva (2013)

Open Mathematics

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The paper contributes to the problem of finding all possible structures and waves, which may arise and preserve themselves in the open nonlinear medium, described by the mathematical model of heat structures. A new class of self-similar blow-up solutions of this model is constructed numerically and their stability is investigated. An effective and reliable numerical approach is developed and implemented for solving the nonlinear elliptic self-similar problem and the parabolic problem....

Global superconvergence of finite element methods for parabolic inverse problems

Hossein Azari, Shu Hua Zhang (2009)

Applications of Mathematics

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In this article we transform a large class of parabolic inverse problems into a nonclassical parabolic equation whose coefficients consist of trace type functionals of the solution and its derivatives subject to some initial and boundary conditions. For this nonclassical problem, we study finite element methods and present an immediate analysis for global superconvergence for these problems, on basis of which we obtain a posteriori error estimators.