this paper considers a class of one-dimensional solidification problem in which kinetic undercooling is incorporated into the temperature condition at the interface. a model problem with nonlinear kinetic law is considered. the main result is an existence theorem. the mathematical effects of the kinetic term are discussed

A simple one-dimensional model for crystal dissolution and precipitation is presented. The model equations resemble a one-phase Stefan problem and involve nonlinear and multi-valued exchange rates at the free boundary. The original equations are formulated on a variable domain. By transforming the model to a fixed domain and applying a regularization, we prove the existence and uniqueness of a ...

A simple 1D model for crystal dissolution and precipitation is presented. The model equations resemble a one-phase Stefan problem and involve non-linear and multivalued exchange rates at the free boundary. The original equations are formulated on a variable domain. By transforming the model to a fixed domain and applying a regularization, we prove the existence and uniqueness of a solution. The...

We consider in this paper the time-dependent two-phase Stefan problem and derive a posteriori error estimates and adaptive strategies for its conforming spatial and backward Euler temporal discretizations. Regularization of the enthalpy–temperature function and iterative linearization of the arising systems of nonlinear algebraic equations are considered. Our estimators yield a guaranteed and f...

In this paper, an application of the Picard's iterative method for finding the solution of two phase Stefan problem is presented. In the proposed method an iterative connection is formulated, which allows to determine the temperature distribution in considered domain. Another unknown function, describing position of the moving interface, is approximated with the aid of linear combination of som...

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...