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From the one-dimensional consolidation of fine-grained soils with threshold gradient, it can be derived a special type of Stefan problems where the seepage front, due to the presence of this threshold gradient, exhibits the features of a…

Analysis of PDEs · Mathematics 2017-03-24 Julieta Bollati , Domingo A. Tarzia

Many metal manufacturing processes involve phase change phenomena, which include melting, boiling, and vaporization. These phenomena often occur concurrently. A prototypical 1D model for understanding the phase change phenomena is the…

Materials Science · Physics 2026-02-11 Yavkreet Swami , Jacob Barajas , Amneet Pal Singh Bhalla

We study the one-dimensional one-phase Stefan problem for the heat equation with a nonlinear boundary condition. We show that all solutions fall into one of three distinct types: global-in-time solutions with exponential decay,…

Analysis of PDEs · Mathematics 2025-10-31 Kensho Araya , Kazuhiro Ishige

Stefan problems relevant to burning oil-water systems are formulated. Two moving boundary sub-problems are defined: burning liquid surface and formation of a distillation ("hot zone") layer beneath it. The basic model considers a heat…

Mathematical Physics · Physics 2010-12-14 Jordan Hristov

The local equilibrium thermodynamics is a basic assumption of macroscopic descriptions of the out of equilibrium dynamics for Hamiltonian systems. We numerically analyze the Hamiltonian Potts model in two dimensions to study the violation…

Statistical Mechanics · Physics 2023-06-21 Michikazu Kobayashi , Naoko Nakagawa , Shin-ichi Sasa

In this paper we consider a one-dimensional one-phase Stefan problem corresponding to the solidification process of a semi-infinite material with a convective boundary condition at the fixed face. The exact solution of this problem,…

Analysis of PDEs · Mathematics 2018-08-09 Julieta Bollati , José A. Semitiel , Domingo A. Tarzia

Within the framework of variational modelling we derive a two-phase moving boundary problem that describes the motion of a semipermeable membrane separating two viscous liquids in a fixed container. The model includes the effects of osmotic…

Analysis of PDEs · Mathematics 2015-03-23 Friedrich Lippoth , Georg Prokert

We consider a semi-infinite one-dimensional phase-change material with two unknown constant thermal coefficients among the latent heat per unit mass, the specific heat, the mass density and the thermal conductivity. Aiming at the…

Mathematical Physics · Physics 2017-04-13 Andrea N. Ceretani , Domingo A. Tarzia

The outflow problem for the viscous full two-phase flow model in a half line is investigated in the present paper. The existence, uniqueness and nonlinear stability of the steady-state are shown respectively corresponding to the supersonic,…

Analysis of PDEs · Mathematics 2022-07-14 Hai-Liang Li , Shuang Zhao , Han-Wen Zuo

An explicit solution of a similarity type is obtained for a one-phase Stefan problem in a semi-infinite material using Kummer functions. Motivated by [D.A. Tarzia, Relationship between Neumann solutions for two phase Lam\'e-Clapeyron-Stefan…

Analysis of PDEs · Mathematics 2016-10-31 Julieta Bollati , Domingo Alberto Tarzia

Following the proposal of steady state thermodynamics (SST) by Oono and Paniconi, we develop a phenomenological theory for steady nonequilibrium states in systems with heat conduction. We find that there is essentially a unique consistent…

Statistical Mechanics · Physics 2007-05-23 Shin-ichi Sasa , Hal Tasaki

Isothermal compressible two-phase flows in a capillary are modeled with and without phase transition in the presence of gravity, employing Darcy's law for the velocity field. It is shown that the resulting systems are thermodynamically…

Analysis of PDEs · Mathematics 2018-07-09 Jan Pruess , Gieri Simonett , Mathias Wilke

The linear dynamics and instability mechanisms of double-layered weakly viscoelastic fluid flowing over an inclined plane are analyzed in the presence of insoluble surfactant at both the free surface and interface. The constitutive equation…

Fluid Dynamics · Physics 2025-10-07 Md. Mouzakkir Hossain , Mohamin B. M. Khan , Youchuang Chao

In this paper we consider two different Stefan problems for a semi-infinite material for the non classical heat equation with a source which depends on the heat flux at the fixed face x = 0. One of them (with constant temperature on x = 0)…

Classical Physics · Physics 2018-10-17 Julieta Bollati , Maria F. Natale , Jose A. Semitiel , Domingo A. Tarzia

We consider a family of multi-phase Stefan problems for a certain 1-d model of cell-to-cell adhesion and diffusion, which takes the form of a nonlinear forward-backward parabolic equation. In each material phase the cell density stays…

Analysis of PDEs · Mathematics 2010-08-04 K. Anguige

The Stefan problem is a classical free-boundary problem that models phase-change processes and poses computational challenges due to its moving interface and nonlinear temperature-phase coupling. In this work, we develop a physics-informed…

Computational Physics · Physics 2025-12-17 Che-Chia Chang , Te-Sheng Lin , Ming-Chih Lai

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

This paper presents results for the sampled-data boundary feedback control to the Stefan problem. The Stefan problem represents a liquid-solid phase change phenomenon which describes the time evolution of a material's temperature profile…

Optimization and Control · Mathematics 2019-06-05 Shumon Koga , Iasson Karafyllis , Miroslav Krstic

The classical Stefan problem, concerning mere heat-transfer during solid-liquid phase transition, is here enhanced towards mechanical effects. The Eulerian description at large displacements is used with convective and Zaremba-Jaumann…

Analysis of PDEs · Mathematics 2023-07-26 Tomáš Roubíček

A two-phase solidification process for a one-dimensional semi-infinite material is considered. It is assumed that it is ensued from a constant bulk temperature present in the vicinity of the fixed boundary, which it is modelled through a…

Analysis of PDEs · Mathematics 2016-09-16 Andrea N. Ceretani , Domingo A. Tarzia