This review features a survey of some recent developments in asymptotic techniques and
new developments, which are valid not only for weakly nonlinear equations, but also for …

This article presents a Stefan problem including thermal conductivity and heat capacity as
the functions of temperature. At α= β, the exact solutions to the proposed problem are …

In this paper, the application of the homotopy perturbation method for solving the inverse
Stefan problem is presented. This problem consists in the calculation of temperature …

In this paper, a comparison between two methods: the Adomian decomposition method and
the variational iteration method, used for solving the moving boundary problem, is …

Purpose of this paper: In this paper an application of the new method for solving the heat
conduction equation in the heterogeneous cast-mould system, with an assumption of the …

We consider two typical inverse Stefan problems: one is computing a heat flux boundary
condition when the moving boundary ξ (t) is given, and another is recovering an unknown …

In the paper, we solve two Stefan problems. The first problem recovers an unknown moving
boundary by specifying the Cauchy boundary conditions on a fixed left-end. The second …

In this paper, we consider the inverse one-phase one-dimensional Stefan problem to study
the thermal processes with phase change in a moving boundary problem and calculate the …

We solve a twofold ill-posed inverse problem of a nonlinear convection-diffusion equation,
endowed with unknown source term and unknown moving boundary. When the solution is …

The paper presents an analytic method applied for finding the approximate solution of
Stefan problem reduced to the one-phase solidification problem of a plate with the unknown …