We consider a one-dimensional one-phase inverse Stefan problem for the heat equation. It consists in recovering boundary influx condition from knowledge of position moving front and initial state. derived logarithmic stability estimate that shows inversion may be severely ill-posed. The proof is based on integral equations unique continuation holomorphic functions. also proposed direct algorith...

When using a polynomial approximating function the most contentious aspect of the Heat Balance Integral Method is the choice of power of the highest order term. In this paper we employ a method recently developed for thermal problems, where the exponent is determined during the solution process, to analyse Stefan problems. This is achieved by minimising an error function. The solution requires ...

In this article, Adomian decomposition method is successfully applied to find an approximate analytical solution of a Stefan problem subject to periodic boundary condition. By using initial and boundary conditions, the explicit solutions of the temperature distribution and the position of moving interface are evaluated and numerical results are depicted graphically. The method performs extremel...

In this article, Adomian decomposition method is successfully applied to find an approximate analytical solution of a Stefan problem subject to periodic boundary condition. By using initial and boundary conditions, the explicit solutions of the temperature distribution and the position of moving interface are evaluated and numerical results are depicted graphically. The method performs extremel...

We prove the existence and uniqueness, local in time, of a solution for a one-phase Stefan problem of a non-classical heat equation for a semiinfinite material with temperature boundary condition at the fixed face. We use the Friedman-Rubinstein integral representation method and the Banach contraction theorem in order to solve an equivalent system of two Volterra integral equations.

A moving, solidifying interface that grows by the instantaneous adsorption of a diffusing solute is described by the classic one-sided “Stefan problem” [15, 19]. More generally, the behavior of precipitate growth can depend on both surface kinetics and bulk drift of the depositing species. We generalize the Stefan problem and its interface boundary condition to explicitly account for both surfa...

A moving, solidifying interface that grows by the instantaneous adsorption of a diffusing solute can be described by equations analogous to those of the classical one-sided Stefan problem for solidification. However, the behavior of precipitate growth by material deposition can depend on both surface kinetics and bulk drift of the depositing species. We generalize the Stefan problem and its int...

Brent Hoon (Brent ByungHoon Kang, UNC at Charlotte) said that although Conficker had been contained (by buying up the domain names to be used in C&C) in 2009, Conficker has never disappeared. They are still seeing hits, and there appear to be about six million IP addresses that show signs of infection. Stefan Savage wondered how you could economically get patches to six million people. Someone ...