English
Related papers

Related papers: An inverse problem for the one-phase Stefan proble…

200 papers

In this article we study a mathematical model of the heat transfer in semi infinite material with a variable cross section, when the radial component of the temperature gradient can be neglected in comparison with the axial component is…

Analysis of PDEs · Mathematics 2022-07-05 Targyn A. Nauryz , Adriana C. Briozzo

In this article it is proved the existence of similarity solutions for a one-phase Stefan problem with temperature-dependent thermal conductivity and a Robin condition at the fixed face. The temperature distribution is obtained through a…

Analysis of PDEs · Mathematics 2017-06-22 Andrea N. Ceretani , Natalia N. Salva , Domingo A. Tarzia

A one phase Stefan problem in nonlinear conduction is considered. The problem is shown to admit a unique solution for small times. An exact solution is obtained which is a travelling front moving with constant speed.

Mathematical Physics · Physics 2007-05-23 S. de Lillo , M. C. Salvatori

A mathematical model for a one-phase change problem (particularly a Stefan problem) with a memory flux, is obtained. The hypothesis that the weighted sum of fluxes back in time is proportional to the gradient of temperature is considered.…

Analysis of PDEs · Mathematics 2018-10-18 Sabrina Roscani , Julieta Bollati , Domingo Tarzia

We study the nonlocal Stefan problem, where the phase transition is described by a nonlocal diffusion as well as the change of enthalpy functions. By using a stochastic optimization approach introduced for the local case, we construct…

Analysis of PDEs · Mathematics 2026-04-21 Raymond Chu , Inwon Kim , Young-Heon Kim , Kyeongsik Nam

This paper develops an input-to-state stability (ISS) analysis of the Stefan problem with respect to an unknown heat loss. The Stefan problem represents a liquid-solid phase change phenomenon which describes the time evolution of a…

Optimization and Control · Mathematics 2019-03-06 Shumon Koga , Iasson Karafyllis , Miroslav Krstic

We construct examples for the one-phase Stefan problem which show that $\alpha$-concavity of the solution is in general not preserved in time, for $0 \le \alpha <1/2$. In particular, this shows that, in contrast to the case of the heat…

Analysis of PDEs · Mathematics 2021-11-17 Albert Chau , Ben Weinkove

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

We study a nonlocal version of the two-phase Stefan problem, which models a phase transition problem between two distinct phases evolving to distinct heat equations. Mathematically speaking, this consists in deriving a theory for…

Analysis of PDEs · Mathematics 2013-07-05 Emmanuel Chasseigne , Silvia Sastre-Gomez

In this paper a one-phase Stefan problem with size-dependent thermal conductivity is analysed. Approximate solutions to the problem are found via perturbation and numerical methods, and compared to the Neumann solution for the equivalent…

Other Condensed Matter · Physics 2019-01-04 Francesc Font

In this paper, a one-phase Stefan-type problem for a semi-infinite material which has as its main feature a variable latent heat that depends on the power of the position and the velocity of the moving boundary is studied. Exact solutions…

Analysis of PDEs · Mathematics 2018-10-24 Julieta Bollati , Domingo A. Tarzia

This paper delves into the Inverse Stefan problem, specifically focusing on determining the time-dependent source coefficient in the parabolic heat equation governing heat transfer in a semi-infinite rod. The problem entails the intricate…

Analysis of PDEs · Mathematics 2025-01-22 Targyn A. Nauryz , Khumoyun Jabbarkhanov

We consider a new Stefan-type problem for the classical heat equation with a latent heat and phase-change temperature depending of the variable time. We prove the equivalence of this Stefan problem with a class of boundary value problems…

Analysis of PDEs · Mathematics 2022-07-20 Adriana C. Briozzo , Colin Rogers , Domingo A. Tarzia

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

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

Recently it was obtained in [Tarzia, Thermal Sci. 21A (2017) 1-11] for the classical two-phase Lam\'e-Clapeyron-Stefan problem an equivalence between the temperature and convective boundary conditions at the fixed face under a certain…

Mathematical Physics · Physics 2018-10-17 Julieta Bollati , Domingo A. Tarzia

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

This contribution presents a backstepping-based state feedback design for the tracking control of a two-phase Stefan problem which is encountered in the Vertical Gradient Freeze crystal growth process. A two-phase Stefan problem consists of…

Optimization and Control · Mathematics 2025-02-14 Stefan Ecklebe , Frank Woittennek , Jan Winkler

In this article we consider a mathematical model of an initial stage of closure electrical contact that involves a metallic vaporization after instantaneous exploding of contact due to arc ignition with power $P_0$ on fixed face $z=0$ and…

Analysis of PDEs · Mathematics 2022-07-20 T. A. Nauryz

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