Related papers: A Stefan problem on an evolving surface
This paper revisits the well-studied fixed point problem from a unified viewpoint of mathematical modeling and canonical duality theory, i.e. the original problem is first reformulated as a nonconvex optimization problem, its well-posedness…
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…
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…
We investigate the existence, uniqueness, and $L^1$-contractivity of weak solutions to a porous medium equation with fractional diffusion on an evolving hypersurface. To settle the existence, we reformulate the equation as a local problem…
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…
We present iterative solvers to approximate the solution of numerical schemes for stochastic Stefan problems. After briefly talking about the convergence results, we tackle the question of efficient strategies for solving the nonlinear…
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…
We consider a setting in which an evolving surface is implicitly characterized as the zero level of a level set function. Such an implicit surface does not encode any information about the path of a single point on the evolving surface. In…
We consider the nonlinear Stefan problem $$ \left \{ \begin{array} {ll} -d \Delta u=a u-b u^2 \;\; & \mbox{for } x \in \Omega (t), \; t>0, \\ u=0 \mbox{ and } u_t=\mu|\nabla_x u |^2 \;\;&\mbox{for } x \in \partial\Omega (t), \; t>0, \\…
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…
We prove locally in time the existence of a smooth solution for multidimensional two-phase Stefan problem for degenerate parabolic equations of the porous medium type. We establish also natural H\"{o}lder class for the boundary conditions…
A general purely crystalline mean curvature flow equation with a nonuniform driving force term is considered. The unique existence of a level set flow is established when the driving force term is continuous and spatially Lipschitz…
The Stefan problem with surface tension is well known to exhibit discontinuities in the associated moving aggregate (i.e., in the domain occupied by the solid), whose structure has only been understood under translational or radial symmetry…
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…
A system of partial differential equations representing stochastic neural fields was recently proposed with the aim of modelling the activity of noisy grid cells when a mammal travels through physical space. The system was rigorously…
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,…
In this paper we propose a new method to stabilise non-symmetric indefinite problems. The idea is to solve a forward and an adjoint problem simultaneously using a suitable stabilised finite element method. Both stabilisation of the element…
We consider the one-dimensional outer stochastic Stefan problem with reflection. The problem admits maximal solutions as long as the velocity of the moving boundary remains bounded, [3,9,10]. We apply Malliavin calculus to the transformed…
Stability is a key property of both forward models and inverse problems, and depends on the norms considered in the relevant function spaces. For instance, stability estimates for hyperbolic partial differential equations are often based on…
A range of optimization cases of two-dimensional Stefan problems, solved using a tracking-type cost-functional, is presented. A level set method is used to capture the interface between the liquid and solid phases and an immersed boundary…