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Different one-phase Stefan problems for a semi-infinite slab are considered, involving a moving phase change material as well as temperature dependent thermal coefficients. Existence of at least one similarity solution is proved imposing a…

Analysis of PDEs · Mathematics 2021-05-12 Julieta Bollati , Adriana C. Briozzo

The technique of periodic homogenization with two-scale convergence is applied to the analysis of a two-phase Stefan-type problem that arises in the study of a periodic array of melting ice bars. For this "reduced model" we prove results on…

Analysis of PDEs · Mathematics 2014-11-13 Isabell Graf , John M. Stockie

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 establish certain oscillation estimates for weak solutions to nonlinear, anomalous phase transitions modeled on the nonlocal two-phase Stefan problem. The problem is singular in time, is scaling deficient and influenced by far-off…

Analysis of PDEs · Mathematics 2025-04-25 Kyeongbae Kim , Ho-Sik Lee , Harsh Prasad

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

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

We consider two implicit approximation schemes of the one-dimensional supercooled Stefan problem and prove their convergence, even in the presence of finite time blow-ups. All proofs are based on a probabilistic reformulation recently…

Numerical Analysis · Mathematics 2022-06-30 Christa Cuchiero , Christoph Reisinger , Stefan Rigger

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 study self-similar solutions of a multi-phase Stefan problem for a heat equation on the half-line $x>0$ with a constant initial data and with Dirichlet or Neumann boundary conditions. In the case of Dirichlet boundary condition we prove…

Analysis of PDEs · Mathematics 2024-05-22 E. Yu. Panov

This paper presents a control design for the one-phase Stefan problem under actuator delay via a backstepping method. The Stefan problem represents a liquid-solid phase change phenomenon which describes the time evolution of a material's…

Optimization and Control · Mathematics 2019-01-29 Shumon Koga , Delphine Bresch-Pietri , Miroslav Krstic

The supercooled Stefan problem and its variants describe the freezing of a supercooled liquid in physics, as well as the large system limits of systemic risk models in finance and of integrate-and-fire models in neuroscience. Adopting the…

Probability · Mathematics 2022-03-21 Vadim Kaushansky , Christoph Reisinger , Mykhaylo Shkolnikov , Zhuo Qun Song

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

We provide perturbative estimates for the one-phase Stefan free boundary problem and obtain the regularity of flat free boundaries via a linearization technique in the spirit of the elliptic counterpart established by the first author.

Analysis of PDEs · Mathematics 2020-07-20 Daniela De Silva , Nicolo Forcillo , Ovidiu Savin

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

This paper develops a control and estimation design for the one-phase Stefan problem. The Stefan problem represents a liquid-solid phase transition as time evolution of a temperature profile in a liquid-solid material and its moving…

Optimization and Control · Mathematics 2017-03-20 Shumon Koga , Mamadou Diagne , Miroslav Krstic

A one-dimensional fractional one-phase Stefan problem with a temperature boundary condition at the fixed face is considered. An integral relationship between the temperature and the free boundary is obtained which is equivalent to the…

Analysis of PDEs · Mathematics 2018-10-25 Sabrina Roscani , Domingo Tarzia

This paper is devoted to present an approximation of a Cauchy problem for Friedrichs' systems under convex constraints. It is proved the strong convergence in L^2\_{loc} of a parabolic-relaxed approximation towards the unique constrained…

Analysis of PDEs · Mathematics 2015-06-01 Jean-François Babadjian , Clément Mifsud , Nicolas Seguin

We show the convergence of the zero relaxation limit in systems of $2 \times 2$ hyperbolic conservation laws with stochastic initial data. Precisely, solutions converge to a solution of the local equilibrium approximation as the relaxation…

Analysis of PDEs · Mathematics 2018-11-01 James M. Scott , M. Paul Laiu , Cory D. Hauck

We prove existence and uniqueness of strong solutions to the two-phase Stefan problem with Gibbs-Thomson law where the free interface forms a ninety degree contact angle with the fixed boundary. We also discuss existence of global solutions…

Analysis of PDEs · Mathematics 2020-01-20 Maximilian Rauchecker

We consider the inverse multiphase Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundaries. Optimal control framework is pursued, where boundary…

Analysis of PDEs · Mathematics 2019-09-23 Ugur G. Abdulla , Bruno Poggi