Consider a unidimensional, single-phase nonlinear Stefan problem with nonlinear source and permeance terms, and a Dirichlet boundary condition depending on the free-boundary function. This problem is important in groundwater ow. By immobilizing the free-boundary with the help of a Landau type transformation, together with a homogeneous transformation dealing with the nonhomogeneous Dirichlet bo...

In this paper the possibility of application of the Adomian decomposition method for solving the moving boundary problem is presented. As an example of the moving boundary problem we consider a one-phase Stefan problem with Neumann’s boundary condition. This problem consists of finding the distribution of temperature in the domain and position of the moving interface. The validity of the approa...

Keywords: Level set method Epitaxial growth Diffusion Stefan problem Sharp interface Robin boundary condition a b s t r a c t We present a numerical method for simulating diffusion dominated phenomena on irregular domains and free moving boundaries with Robin boundary conditions on quadtree/ octree adaptive meshes. In particular, we use a hybrid finite-difference and finite-volume framework tha...

References: 1) Husain Aljazzar and Stefan Leue: Debugging of Dependability Models Using Interactive Visualization of Counterexamples, to appear in proceedings of QEST 2008. 2) Husain Aljazzar and Stefan Leue: Directed explicit state-space search in the generation of counterexamples for probabilistic reachability, 2008, submitted for journal publication. 3) Husain Aljazzar and Stefan Leue: Count...

Keywords: Stefan problem Non-classical heat equation Free boundary problem Similarity solution Nonlinear heat sources Volterra integral equation a b s t r a c t We prove the existence and uniqueness, local in time, of the solution of a one-phase Stefan problem for a non-classical heat equation for a semi-infinite material with a convective boundary condition at the fixed face x = 0. Here the he...

We prove that classical C 1-solutions to phase transition problems, which include the two-phase Stefan problem, are smooth. The problem is reduced to a xed domain using von Mises variables. The estimates are obtained by frozen coeecients and new L p estimates for linear parabolic equations with dynamic boundary condition. Crucial ingredients are the observation that a certain function is a Four...

In this article, we study the behavior of two species evolving in a domain with free boundary. This system mimics spread invasive or new predator species, which boundaries represent expanding fronts and are described by Stefan condition. A priori estimates for required functions established. These used to prove existence uniqueness solution.

In this paper we consider the model of phase relaxation introduced in [22], where an asymptotic analysis is performed toward integral formulation Stefan problem when parameter approaches zero. Assuming natural physical assumption that initial condition constrained, but taking more general boundary conditions, prove solution relaxed converges a stronger way to classical weak problem.

The Stefan problem with small surface tension e is considered. Assuming that the classical Stefan problem (with s = 0) has a smooth free boundary T, we denote the temperature of the solution by 60 and consider an approximate solution 60 + su for the case where e ^ 0, e small. We first establish the existence and uniqueness of u , and then investigate the effect of u on the free boundary T. It i...