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Related papers: Large-time behavior of one-phase Stefan-type probl…

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The focus of our work is dispersive, second-order effective model describing the low-frequency wave motion in heterogeneous (e.g.~functionally-graded) media endowed with periodic microstructure. For this class of quasi-periodic medium…

Numerical Analysis · Mathematics 2020-06-05 Danial P. Shahraki , Bojan B. Guzina

We consider a lattice regularization for an ill-posed diffusion equation with trilinear constitutive law and study the dynamics of phase interfaces in the parabolic scaling limit. Our main result guarantees for a certain class of…

Analysis of PDEs · Mathematics 2020-03-13 Michael Helmers , Michael Herrmann

In this paper we formulate a Stefan problem appropriate when the thermophysical properties are distinct in each phase and the phase-change temperature is size or velocity dependent. Thermophysical properties invariably take different values…

Computational Physics · Physics 2019-04-12 Timothy G. Myers , Matthew G. Hennessy , Marc Calvo-Schwarzwälder

The one-dimensional (1D) Stefan problem is a prototypical heat and mass transfer problem that analyzes the temperature distribution in a material undergoing phase change. In addition, it describes the evolution of the phase change front…

Fluid Dynamics · Physics 2026-02-10 Mehran Soleimani , Kimmo Koponen , Nils Tilton , Amneet Pal Singh Bhalla

A new comprehensive analysis of Stefan's flow caused by a free growing droplet in vapor-gas atmosphere with several condensing components is presented. This analysis, based on the nonstationary heat and material balance and diffusion…

Atmospheric and Oceanic Physics · Physics 2016-09-28 A. E. Kuchma , A. K. Shchekin , D. S. Martyukova

Diffusion in inhomogeneous materials can be described by both the Fick and Fokker--Planck diffusion equations. Here, we study a mixed Fick and Fokker-Planck diffusion problem with coefficients rapidly oscillating both in space and time. We…

Analysis of PDEs · Mathematics 2020-03-17 Micol Amar , Daniele Andreucci , Emilio N. M. Cirillo

The time-fractional diffusion equation is considered, where the time derivative is either of Caputo or Riemann-Liouville type. The solution of a general initial-boundary value problem with time-dependent boundary conditions over bounded and…

Analysis of PDEs · Mathematics 2023-01-04 M. Rodrigo

In this paper, a backstepping control of the one-phase Stefan Problem, which is a 1-D diffusion Partial Differential Equation (PDE) defined on a time varying spatial domain described by an ordinary differential equation (ODE), is studied. A…

Optimization and Control · Mathematics 2016-07-18 Shumon Koga , Mamadou Diagne , Shuxia Tang , Miroslav Krstic

We consider approximations of the Stefan-type condition by imbalances of volume closely around the inner interface and study convergence of the solutions of the corresponding semilinear stochastic moving boundary problems. After a…

Probability · Mathematics 2018-10-29 Marvin S. Mueller

We pursue a low-wavenumber, second-order homogenized solution of the time-harmonic wave equation at both low and high frequency in periodic media with a source term whose frequency resides inside a band gap. Considering the wave motion in…

Analysis of PDEs · Mathematics 2021-02-23 Shixu Meng , Othman Oudghiri-Idrissi , Bojan B. Guzina

Spatial inhomogeneity, temporal modulation, and engineered anisotropy of parameters of electromagnetic media offer numerous opportunities for manipulating light-matter interaction over the past decades. Here, we investigate a scenario in…

Similarity solutions for a one-dimensional mathematical model for thawing in a saturated semi-infinite porous media is considered when change of phase induces a density jump and a convective boundary condition is imposed at the fixed face…

Analysis of PDEs · Mathematics 2014-05-22 Andrea N. Ceretani , Domingo A. Tarzia

We analyze the behavior of solutions of the Poisson equation with homogeneous Neumann boundary conditions in a two-dimensional thin domain which presents locally periodic oscillations at the boundary. The oscillations are such that both the…

Analysis of PDEs · Mathematics 2018-01-30 José M. Arrieta , Manuel Villanueva-Pesqueira

The present paper concerns a space-time homogenization problem for nonlinear diffusion equations with periodically oscillating (in space and time) coefficients. Main results consist of corrector results (i.e., strong convergences of…

Analysis of PDEs · Mathematics 2022-10-26 Tomoyuki Oka

The asymptotic behavior of the solution of an infinite set of Smoluchowski's discrete coagulation-fragmentation-diffusion equations with non-homogeneous Neumann boundary conditions, defined in a periodically perforated domain, is analyzed.…

Mathematical Physics · Physics 2017-11-17 Laurent Desvillettes , Silvia Lorenzani

We derive various novel free boundary problems as limits of a coupled bulk-surface reaction-diffusion system modelling ligand-receptor dynamics on evolving domains. These limiting free boundary problems may be formulated as Stefan-type…

Analysis of PDEs · Mathematics 2024-07-24 Amal Alphonse , Diogo Caetano , Charles M. Elliott , Chandrasekhar Venkataraman

This study investigates the melting process of a three-phase Stefan problem in a semi-infinite material, imposing a convective boundary condition at the fixed face. By employing a similarity-type transformation, the problem is reduced to a…

Analysis of PDEs · Mathematics 2025-02-11 Julieta Bollati , María Fernanda Natale , José Abel Semitiel , Domingo Alberto Tarzia

Hypothesis:Diffusion in confinement is an important fundamental problem with significant implications for applications of supported liquid phases. However, resolving the spatially dependent diffusion coefficient, parallel and perpendicular…

The two-phase Stefan problem describes the temperature distribution in a homogeneous medium undergoing a phase transition such as ice melting to water. This is accomplished by solving the heat equation on a time-dependent domain, composed…

Analysis of PDEs · Mathematics 2016-07-05 Mahir Hadzic , Gustavo Navarro , Steve Shkoller

We study classical particles on the sites of an open chain which diffuse, coagulate and decoagulate preferentially in one direction. The master equation is expressed in terms of a spin one-half Hamiltonian $H$ and the model is shown to be…

Condensed Matter · Physics 2015-06-25 Haye Hinrichsen , Klaus Krebs , Ingo Peschel