The only source of ice formation in the Arctic during summer is a layer of ice between an under-ice melt pond and the underlying ocean, called false-bottoms. The simultaneous growth and ablation of false-bottoms is governed by both of heat fluxes and salt fluxes. This is a two-phase Stefan problem with two free boundaries. We first use Green functions to reduce this problem to solving a system ...

This paper investigates the integrated optimization of production, distribution and inventory decisions related to supplying multiple retailers from a central production facility. A single-item uncapacitated lot-sizing problem is defined for optimizing production decisions and inventory management. The optimization of daily distribution is modeled as a traveling salesman problem or a vehicle ro...

Two models of recrystallization are proposed taking into account the convective flux impurity exchange between polycrystalline and thin-film coating. The special boundary modes described by single-phase two-phase Stefan problems with condition at coated surface containing term. exact solutions formulated corresponding to grain-boundary concentration impurities obtained. detail theoretical analy...

Temperature and phase evolution in phase transitions are represented here by coupling the energy balance equation with a multivalued constitutive relation between the density of internal energy and the temperature, and with a nonlinear conduction law. This doubly nonlinear problem generalizes the classical Stefan model. Existence of a weak solution is proved via time discretization, a priori es...

We investigate pattern formation in a two-dimensional (2D) Fisher–Stefan model, which involves solving the Fisher–KPP equation on compactly-supported region with moving boundary. The boundary evolves analogously to classical one-phase Stefan problem, such that speed is proportional local population density gradient. By combining and theory, model alleviates two limitations of for biological pop...

The Stefan problem is one of the best known parabolic two-phase free boundary problems. It is a simple model of phase transitions in liquid-solid systems. Let Ω⊂Rn denote a domain that contains a liquid and a solid separated by an interface Γ. As the melting or cooling take place the boundary moves and we are naturally led to a free boundary problem. The unknowns are the temperatures of the liq...

We study minimizers of the functional ∫ B 1 |∇u|xn dx+ 2 ∫ B′ 1 (λ+u + + λ−u −) dx′, for a ∈ (−1, 1). The problem arises in connection with heat flow with control on the boundary. It can also be seen as a non-local analogue of the, by now well studied, two-phase obstacle problem. Moreover, when u does not change signs this is equivalent to the fractional obstacle problem. Our main results are t...

We consider a coupled system of parabolic/ODE equations describing solid combustion. For a given rescaling of the reaction term (the high activation energy limit), we show that the limit solution solves a free boundary problem which is to our knowledge new. In the time-increasing case, the limit coincides with the Stefan problem with spatially inhomogeneous coefficients. In general it is a para...