Related papers: Weak Stefan Formulation for Bulk Crystal Growth wi…
We study the stochastic Willmore flow and the stochastic surface diffusion flow for closed or non-closed curves on $\mathbb{R}^2$ in this paper. We equivalently formulate them as a stochastic one-phase Stefan problem (or a stochastic free…
This paper establishes the existence, uniqueness and time-space regularity of the weak solution to a nonlinear coupled parabolic system modeling temperature evolution in a coaxial heat exchanger with source terms and spatially varying…
This work is aimed at the study and analysis of the heat transport on a metal bar of length $L$ with a solid-solid interface. The process is assumed to be developed along one direction, across two homogeneous and isotropic materials.…
We investigate a family of phase field models for simulating dendritic growth of a pure supercooled substance. The central object of interest is the reaction term in the Allen-Cahn equation, which is responsible for spatial distribution of…
We study the motion of phase interfaces in a diffusive lattice equation with bistable nonlinearity and derive a free boundary problem with hysteresis to describe the macroscopic evolution in the parabolic scaling limit. The first part of…
Strongly correlated systems far from equilibrium can exhibit scaling solutions with a dynamically generated weak coupling. We show this by investigating isolated systems described by relativistic quantum field theories for initial…
The financial model proposed involves the liquidation process of a portfolio of $n$ assets through sell or (and) buy orders with volatility. We present the rigorous mathematical formulation of this model in a financial setting resulting to…
In this paper, an elegant mathematical approach is introduced to solve the equations of warm inflationary model without using extra approximations other than slow-roll. This important inflationary method known as Hamilton-Jacobian…
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 discuss applications of a recently developed method for model reduction based on linear response theory of weakly coupled dynamical systems. We apply the weak coupling method to simple stochastic differential equations with slow and fast…
We present an abstract framework for analyzing the weak error of fully discrete approximation schemes for linear evolution equations driven by additive Gaussian noise. First, an abstract representation formula is derived for sufficiently…
This paper is dedicated to the solidification of a water drop impacting a cold solid surface. In a first part, we establish a 1D solidification model, derived from the Stefan problem, that aims at predicting the freezing dynamic of a liquid…
We give an updated overview of both weak and strong coupling methods to describe the approach to a plasma described by viscous hydrodynamics, a process now called hydrodynamisation. At weak coupling the very first moments after a heavy ion…
In this work, we introduce a notion of dissipative weak solution for a system describing the evolution of a heat-conducting incompressible non-Newtonian fluid. This concept of solution is based on the balance of entropy instead of the…
Solving the Stefan problem, also referred as the heat conduction problem with phase change, is a necessary step to solve phase change problems with convection. In this article, we are interested in using the Lattice Boltzmann Method (LBM)…
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…
We prove uniqueness of the maximal weak solutions to the supercooled Stefan problem in 1 dimension. This follows by showing that in 1 dimension, the optimal solution of the corresponding free target optimal transport problem given in…
We consider a special type of fast reaction-diffusion systems in which the coefficients of the reaction terms of the two substances are much larger than those of the diffusion terms while the diffusive motion to the substrate is negligible.…
We report logarithmically slow expansion of hot bubbles in gases in the process of cooling. A model problem first solved, when the temperature has compact support. Then temperature profile decaying exponentially at large distances is…
This paper examines the well-posedness of the Stefan problem with a dynamic boundary condition. To show the existence of the weak solution, the original problem is approximated by a limit of an equation and dynamic boundary condition of…