We reduce the two phase Stefan problem with kinetic to a system of nonlinear Volterra integral equations of second kind and apply Newton's method to linearize it. We found product integration solution of the linear form. Sufficient conditions for convergence of the numerical method are given and their applicability is illustrated with an example.

Stefan problem with kinetics is reduced to a system of nonlinear Volterra integral equations of second kind and Newton's method is applied to linearize it. Product integration solution of the linear form is found and sufficient conditions for convergence of the numerical method are given. An example is provided to illustrated the applicability of the method.

Taking into account the recent works \cite{RoTaVe:2020} and \cite{Rys:2020}, we consider a phase-change problem for one dimensional material with non-local flux, expressed in terms of Caputo derivative, which derives space-fractional Stefan problem. We prove existence unique solution to fractional Neumann boundary condition at fixed face $x=0$, where domain, initial time, consists liquid solid....

We would like to thank Brian Kantor, Jim Madden, and Pat Wilson of UCSD for technical support of the Network Telescope project; Mike Gannis, Nicholas Weaver, Wendy Garvin, Team Cymru, and Stefan Savage for feedback on this document; and the Cisco PSIRT Team, Wendy Garvin, Team Cymru, Nicholas Weaver, and Vern Paxson for discussion as events unfolded. Support for this work was provided by Cisco ...

Several years ago, Stefan Pokorski, Manfred Münz and us outlined a program for calculation of the NLO QCD corrections to the weak radiative B̄ meson decay B̄ → Xsγ. Very recently, just before the 60th birthday of Stefan Pokorski, this program has been formally completed. In the present paper, we summarize the existing results and discuss perspectives for further improvement of the accuracy of the...

We consider both stationary and time dependent heat equation for a non-convex body or a collection of disjoint conductive bodies with Stefan-Boltzmann radiation condition on the surface. The main virtue of the resulting problem is non-locality of the boundary condition due to self-illuminating radiation on the surface. Moreover, the problem is non-linear and in the general case also non-coerciv...

We study a one-phase Stefan problem for a semi-infinite material with temperaturedependent thermal conductivity and a convective term with a constant temperature boundary condition or a heat flux boundary condition of the type −q0/ √ t (q0 > 0) at the fixed face x = 0. We obtain in both cases sufficient conditions for data in order to have a parametric representation of the solution of the simi...

We study steady states of Stefan-type problems in the plane with the Gibbs-Thomson correction involving general anisotropic energy density function. By a local analysis we prove the global result showing that the solution is the Wulff shape. The key element is a stability result which enables us to approximate singular models by regulars ones. keywords: Stefan-type problems, singular interfacia...