Related papers: An inverse problem for the one-phase Stefan proble…
Moving boundary problems allow to model systems with phase transition at an inner boundary. Driven by problems in economics and finance, in particular modeling of limit order books, we consider a stochastic and non-linear extension of the…
We study the large-time behavior of solutions of a one-phase Stefan-type problem with anisotropic diffusion in periodic media on an exterior domain in a dimension $n \geq 3$. By a rescaling transformation that matches the expansion of the…
We propose an improved model explaining the occurrence of high stresses due to the difference in specific volumes during phase transitions between water and ice. The unknowns of the resulting evolution problem are the absolute temperature,…
We present a finite-element approximation for the one-sided Stefan problem and the one-sided Mullins--Sekerka problem, respectively. The problems feature a fully anisotropic Gibbs--Thomson law, as well as kinetic undercooling. Our…
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…
Inverse Stefan problem arising in modeling of laser ablation of biomedical tissues is analyzed, where information on the coefficients, heat flux on the fixed boundary, and density of heat sources are missing and must be found along with the…
In this work, we consider the outer Stefan problem for the short-time prediction of the spread of a volatile asset traded in a financial market. The stochastic equation for the evolution of the density of sell and buy orders is the Heat…
Dendrites are one of the most widely observed patterns in nature and occur across a wide spectrum of physical phenomena. In solidification and growth patterns in metals and crystals, the multi-level branching structures of dendrites pose a…
The dissolution of solids has created spectacular geomorphologies ranging from centimeter-scale cave scallops to the kilometer-scale "stone forests" of China and Madagascar. Mathematically, dissolution processes are modeled by a Stefan…
We study the distribution of the Schmidt coefficients of the reduced density matrix of a quantum system in a pure state. By applying general methods of statistical mechanics, we introduce a fictitious temperature and a partition function…
We review some fractional free boundary problems that were recently considered for modeling anomalous phase-transitions. All problems are of Stefan type and involve fractional derivatives in time according to Caputo's definition. We survey…
We investigate the one-dimensional growth of a solid into a liquid bath, starting from a small crystal, using the Guyer-Krumhansl and Maxwell-Cattaneo models of heat conduction. By breaking the solidification process into the relevant time…
The problem of melting a crystal dendrite is modelled as a quasi-steady Stefan problem. By employing the Baiocchi transform, asymptotic results are derived in the limit that the crystal melts completely, extending previous results that hold…
An inverse source problem for the heat equation is considered. Extraction formulae for information about the time and location when and where the unknown source of the equation firstly appeared are given from a single lateral boundary…
From the final and interior temperature measurements identifying the source term with initial temperature simultaneously is an inverse heat conduction problem which is a kind of ill-posed. The optimal control framework has been found to be…
In this work, we consider the fractional Stefan-type problem in a Lipschitz bounded domain $\Omega\subset\mathbb{R}^d$ with time-dependent Dirichlet boundary condition for the temperature $\vartheta=\vartheta(x,t)$, $\vartheta=g$ on…
We present a simple, analytic point source model for both static and time-varying point-like heat sources and the resulting temperature profile that solves the heat equation in dimension three. Simple algorithms to detect the location and…
Motivated by applications in economics and finance, in particular to the modeling of limit order books, we study a class of stochastic second-order PDEs with non-linear Stefan-type boundary interaction. To solve the equation we transform…
Free boundary problems appear naturally in numerous areas of mathematics, science and engineering. These problems present a great computational challenge because they necessitate numerical methods that can yield an accurate approximation of…
We develop an enthalpy-based modeling and computational framework to quantify uncertainty in Stefan problems with an injection boundary. Inspired by airfoil icing studies, we consider a system featuring an injection boundary inducing domain…