Related papers: A nonlocal one-phase Stefan problem that develops …
We introduce a notion of viscosity solutions for the two-phase Stefan problem, which incorporates possible existence of a mushy region generated by the initial data. We show that a comparison principle holds between viscosity solutions, and…
This work is devoted to the proof of the existence of a martingale solution for a complex version of the stochastic Stefan problem. This particular formulation incorporates two important features: a mushy region and turbulent transport…
This work establishes a scaling limit theorem for the Stefan problem incorporating a mushy region, demonstrating that solutions to stochastic variants with turbulent transport terms converge to the solution to a deterministic partial…
The qualitative behavior of a thermodynamically consistent two-phase Stefan problem with surface tension and with or without kinetic undercooling is studied. It is shown that these problems generate local semiflows in well-defined state…
We introduce and analyze a nonlocal version of the one-phase Stefan problem in which, as in the classical model, the rate of growth of the volume of the liquid phase is proportional to the rate at which energy is lost through the…
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…
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…
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…
We consider local solutions of the two-phase Stefan problem with a "mushy" region. We show that if a (distributional) solution u is locally square integrable then the temperature is continuous.
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.
We formulate a Stefan problem on an evolving hypersurface and study the well-posedness of weak solutions given $L^1$ data. To do this, we first develop function spaces and results to handle equations on evolving surfaces in order to give a…
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…
We study self-similar solutions of a multi-phase Stefan problem, first in the case of one space variable, and then in the radial multidimensional case. In both these cases we prove that a nonlinear algebraic system for determination of the…
We study the long-time behavior of solutions of the one-phase Stefan problem in inhomogeneous media in dimensions $n \geq 2$. Using the technique of rescaling which is consistent with the evolution of the free boundary, we are able to show…
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…
We consider a probabilistic formulation of a singular two-phase Stefan problem in one space dimension, which amounts to a coupled system of two McKean-Vlasov stochastic differential equations. In the financial context of systemic risk, this…
The non-local in space two-phase Stefan problem (a prototype in phase change problems) can be formulated via a singular nonlinear parabolic integro-differential equation which admits a unique weak solution. This formulation makes Stefan…
The classical Stefan problem is one of the most studied free boundary problems of evolution type. Recently, there has been interest in treating the corresponding free boundary problem with nonlocal diffusion. We start the paper by reviewing…
A thermodynamically consistent two-phase Stefan problem with temperature-dependent surface tension and with or without kinetic undercooling is studied. It is shown that these problems generate local semiflows in well-defined state…
Environmental processes resolved at a sufficiently small scale in space and time will inevitably display non-stationary behavior. Such processes are both challenging to model and computationally expensive when the data size is large.…