Displaying similar documents to “Asymptotic properties of a semilinear heat equation with strong absorption and small diffusion.”

A Neumann problem for a convection-diffusion equation on the half-line

Piotr Biler, Grzegorz Karch (2000)

Annales Polonici Mathematici

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We study solutions to a nonlinear parabolic convection-diffusion equation on the half-line with the Neumann condition at x=0. The analysis is based on the properties of self-similar solutions to that problem.

Diffusion phenomenon for second order linear evolution equations

Ryo Ikehata, Kenji Nishihara (2003)

Studia Mathematica

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We present an abstract theory of the diffusion phenomenon for second order linear evolution equations in a Hilbert space. To derive the diffusion phenomenon, a new device developed in Ikehata-Matsuyama [5] is applied. Several applications to damped linear wave equations in unbounded domains are also given.

Derivation of a homogenized two-temperature model from the heat equation

Laurent Desvillettes, François Golse, Valeria Ricci (2014)

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

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This work studies the heat equation in a two-phase material with spherical inclusions. Under some appropriate scaling on the size, volume fraction and heat capacity of the inclusions, we derive a coupled system of partial differential equations governing the evolution of the temperature of each phase at a macroscopic level of description. The coupling terms describing the exchange of heat between the phases are obtained by using homogenization techniques originating from [D. Cioranescu,...

Determination of a diffusion coefficient in a quasilinear parabolic equation

Fatma Kanca (2017)

Open Mathematics

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This paper investigates the inverse problem of finding the time-dependent diffusion coefficient in a quasilinear parabolic equation with the nonlocal boundary and integral overdetermination conditions. Under some natural regularity and consistency conditions on the input data the existence, uniqueness and continuously dependence upon the data of the solution are shown. Finally, some numerical experiments are presented.

Heat kernel estimates for critical fractional diffusion operators

Longjie Xie, Xicheng Zhang (2014)

Studia Mathematica

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We construct the heat kernel of the 1/2-order Laplacian perturbed by a first-order gradient term in Hölder spaces and a zero-order potential term in a generalized Kato class, and obtain sharp two-sided estimates as well as a gradient estimate of the heat kernel, where the proof of the lower bound is based on a probabilistic approach.

Weak Serrin-type finite time blowup and global strong solutions for three-dimensional density-dependent heat conducting magnetohydrodynamic equations with vacuum

Huanyuan Li (2023)

Applications of Mathematics

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This paper is concerned with a Cauchy problem for the three-dimensional (3D) nonhomogeneous incompressible heat conducting magnetohydrodynamic (MHD) equations in the whole space. First of all, we establish a weak Serrin-type blowup criterion for strong solutions. It is shown that for the Cauchy problem of the 3D nonhomogeneous heat conducting MHD equations, the strong solution exists globally if the velocity satisfies the weak Serrin's condition. In particular, this criterion is independent...