Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary

Y Du, Z Lin - SIAM Journal on Mathematical Analysis, 2010 - SIAM
In this paper we investigate a diffusive logistic model with a free boundary in one space
dimension. We aim to use the dynamics of such a problem to describe the spreading of a …

Propagation and reaction–diffusion models with free boundaries

Y Du - Bulletin of Mathematical Sciences, 2022 - World Scientific
In this short survey, we describe some recent developments on the modeling of propagation
by reaction-differential equations with free boundaries, which involve local as well as …

Spreading and vanishing in nonlinear diffusion problems with free boundaries.

Y Du, B Lou - Journal of the European Mathematical Society (EMS …, 2015 - ems.press
We study nonlinear diffusion problems of the form ut= uxx+ f (u) with free boundaries. Such
problems may be used to describe the spreading of a biological or chemical species, with …

An SIR epidemic model with free boundary

KI Kim, Z Lin, Q Zhang - Nonlinear Analysis: Real World Applications, 2013 - Elsevier
An SIR epidemic model with free boundary is investigated. This model describes the
transmission of diseases. The behavior of positive solutions to a reaction–diffusion system in …

A moving-boundary problem for concrete carbonation: global existence and uniqueness of weak solutions

A Muntean, M Böhm - Journal of mathematical analysis and applications, 2009 - Elsevier
This paper deals with a one-dimensional coupled system of semi-linear parabolic equations
with a kinetic condition on the moving boundary. The latter furnishes the driving force for the …

Existence of global solutions with slow decay and unbounded free boundary for a superlinear Stefan problem

M Fila, P Souplet - Interfaces and Free Boundaries, 2001 - ems.press
We consider a one-phase Stefan problem for the heat equation with a superlinear reaction
term. It is known from a previous work (Ghidouche, Souplet, & Tarzia [5]) that all global …

A free-boundary problem for concrete carbonation: Front nucleation and rigorous justification of the -law of propagation

T Aiki, A Muntean - Interfaces and Free Boundaries, 2013 - ems.press
A free-boundary problem for concrete carbonation: Front nucleation and rigorous justification
of the pt-law of propagation Page 1 Interfaces and Free Boundaries 15 (2012), 167–180 DOI …

Global existence and blowup of a nonlocal problem in space with free boundary

P Zhou, Z Lin - Journal of Functional Analysis, 2012 - Elsevier
This paper concerns a double fronts free boundary problem for the reaction–diffusion
equation with a nonlocal nonlinear reaction term in space. For such a problem, we mainly …

Numerical approximation of a concrete carbonation model: study of the‐law of propagation

A Zurek - Numerical Methods for Partial Differential Equations, 2019 - Wiley Online Library
In this paper, we are interested in the long time behavior of approximate solutions to a free
boundary model which appears in the modeling of concrete carbonation [1]. In particular, we …

Approximation of random diffusion equations by nonlocal diffusion equations in free boundary problems of one space dimension

Y Du, W Ni - Communications in Contemporary Mathematics, 2023 - World Scientific
We show how the Stefan type free boundary problem with random diffusion in one space
dimension can be approximated by the corresponding free boundary problem with nonlocal …