The ice formation in a water body is examined for the computation of temperature field, phase change and a moving ice-water interface whose location is not known á priori. This is classically referred to as the Stefan problem [Rubinstein, L.I. (1971) The Stefan Problem (American Mathematical Society, Providence, Rhode Island 02904]. Based on the Duvaut [Duvaut, G. (1973) "Résolution d'un problé...

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.

We construct examples for the one-phase Stefan problem which show that $$\alpha $$ -concavity of solution is in general not preserved time, $$0 \le \alpha <1/2$$ . In particular, this shows that, contrast to case heat equation a fixed convex domain, log concavity solutions problem.

The only source of ice formation in the Arctic during summer is a layer of ice called false-bottoms between an under-ice melt pond and the underlying ocean. Of interest is to give a mathematical model in order to determine the simultaneous growth and ablation of false-bottoms, which is governed by both of heat fluxes and salt fluxes. In one dimension, this problem may be considered mathematical...