English
Related papers

Related papers: Sampled-Data Control of the Stefan System

200 papers

We develop a new variational formulation of the inverse Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundary. We employ optimal control framework,…

Analysis of PDEs · Mathematics 2015-06-09 Ugur G. Abdulla

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

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

The present article is dedicated to the forward and backward solution of a transient one-phase Stefan problem. In the forward problem, we compute the evolution of the initial domain for a Stefan problem where the melting temperature varies…

Numerical Analysis · Mathematics 2025-12-17 Marc Dambrine , Helmut Harbrecht

We analyze the state constrained inverse Stefan type parabolic free boundary problem as an optimal control problem in the Sobolev-Besov spaces framework. Boundary heat flux, density of heat sources, and free boundary are components of the…

Analysis of PDEs · Mathematics 2017-12-01 Ugur G. Abdulla , Jonathan Goldfarb , Evan Cosgrove , Curtis Earl

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

We consider a one-dimensional one-phase inverse Stefan problem for the heat equation. It consists in recovering a boundary influx condition from the knowledge of the position of the moving front, and the initial state. We derived a…

Analysis of PDEs · Mathematics 2020-02-24 Chifaa Ghanmi , Saloua Mani-Aouadi , Faouzi Triki

We consider the problem of recovering the initial condition in the one-dimensional one-phase Stefan problem for the heat equation from the knowledge of the position of the melting point. We first recall some properties of the free boundary…

Analysis of PDEs · Mathematics 2021-05-27 Chifaa Ghanmi , Saloua Mani Aouadi , Faouzi Triki

We discuss the feedback control problem for a two-dimensional two-phase Stefan problem. In our approach, we use a sharp interface representation in combination with mesh-movement to track the interface position. To attain a feedback…

Numerical Analysis · Mathematics 2022-12-22 Björn Baran , Peter Benner , Jens Saak

We consider the inverse multiphase Stefan problem with homogeneous Dirichlet boundary condition on a bounded Lipschitz domain, where the density of the heat source is unknown in addition to the temperature and the phase transition…

Analysis of PDEs · Mathematics 2020-05-12 Ugur G. Abdulla , Bruno Poggi

We develop a new variational formulation of the inverse Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundary. We employ optimal control framework,…

Analysis of PDEs · Mathematics 2016-11-01 Ugur G. Abdulla

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 paper provides results for the application of boundary feedback control with Zero-Order-Hold (ZOH) to 1-D linear, first-order, hyperbolic systems with non-local terms on bounded domains. It is shown that the emulation design based on…

Optimization and Control · Mathematics 2017-03-01 Iasson Karafyllis , Miroslav Krstic

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

This paper considers a safe trajectory tracking of the Stefan problem with a second-order moving boundary dynamics. The model is given by a parabolic Partial Differential Equation (PDE) defined on a time-varying domain of moving boundary…

Optimization and Control · Mathematics 2026-05-26 Shumon Koga , Miroslav Krstic

This paper studies the feedback stabilization problem of the motion of a tank that contains an incompressible, Newtonian, viscous liquid. The control input is the force applied on the tank and the overall system consists of two nonlinear…

Optimization and Control · Mathematics 2021-08-26 Iasson Karafyllis , Miroslav Krstic

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

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

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

Optimal sampled-data control of a nonlinear system is considered with the stable-manifold approach and extensive use of numerical techniques. The idea is to notice the Hamiltonian system associated with the considered optimal control…

Systems and Control · Electrical Eng. & Systems 2021-12-30 Yasuaki Oishi , Noboru Sakamoto