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We consider an abstract problem P in a metric space X which has a unique solution u ∈ X. Our aim in this current paper is two folds: first, to provide a convergence criterion to the solution of Problem P, that is, to give necessary and sufficient conditions on a sequence {un} ⊂ X which guarantee the convergence un → u in the space X; second, to find a Tyknonov triple T such that a sequence {un} ⊂ X is a T-approximating sequence if and only if it converges to u. The two problems stated above, associated to the original Problem P, are closely related. We illustrate how they can be solved in three particular cases of Problem P: a variational inequality in a Hilbert space, a fixed point problem in a metric space and a minimization problem in a reflexive Banach space. For each of these problems we state and prove a convergence criterion that we use to define a convenient Tykhonov triple T which requires the condition stated above. We also show how the convergence criterion and the corresponding T -well posedness concept can be used to deduce convergence and classical well-posedness results, respectively. [ABSTRACT FROM AUTHOR]

The work in this paper concerns the study of different approximations for one-dimensional one-phase Stefan-like problems with a space-dependent latent heat. It is considered two different problems, which differ from each other in their boundary condition imposed at the fixed face: Dirichlet and Robin conditions. The approximate solutions are obtained by applying the heat balance integral method (HBIM), the modified HBIM and the refined integral method (RIM). Taking advantage of the exact analytical solutions, we compare and test the accuracy of the approximate solutions. The analysis is carried out using the dimensionless generalised Stefan number (Ste) and Biot number (Bi). It is also studied the case when Bi goes to infinity in the problem with a convective condition, recovering the approximate solutions when a temperature condition is imposed at the fixed face. Some numerical simulations are provided in order to assert which of the approximate integral methods turns out to be optimal. Moreover, we pose an approximate technique based on minimising the least-squares error, obtaining also approximate solutions for the classical Stefan problem. [ABSTRACT FROM AUTHOR]

The goal of this article is to find a correct approximated solution using a polynomial of sixth degree for the free boundary problem corresponding to the diffusion of oxygen in a spherical medium with simultaneous absorption at a constant rate, and to show some mistakes in previously published solutions. [ABSTRACT FROM AUTHOR]

Various authors with small variations have used different expressions in order to compute the nutrient uptake for crop roots. These expressions use the nutrient concentration on the root surface and the corresponding influx, which are computed through various numerical models. This study proposes an alternative formula that uses the nutrient concentration computed by a moving boundary model. The formula output was compared with measured uptake of some nutrients in different crops and soils by using experimental data extracted from the literature. The values obtained were compared with predicted uptakes by other numerical estimations as the Barber-Cushman model and our moving boundary model by using the Cushman uptake formula. Better predictions with respect to a single nutrient were obtained for the cases tested. Moreover, an algorithm to computing the nutrient uptake is also given. [ABSTRACT FROM AUTHOR]

This paper deals with a free-moving boundary diffusion model which describes a catalytic diffusion-reaction process in a gas-solid system with catalyst decay. We consider a one-phase free boundary diffusion problem for the gaseous poison reactant and a two-phase moving boundary diffusion problem for the main gas reactant. We prove a local result in time for the existence and uniqueness of the solution of the corresponding free-moving boundary diffusion problem. [ABSTRACT FROM AUTHOR]

A study on similarity solutions for a mathematical model for thawing in a saturated porous medium is considered when change of phase induces a density jump and the influence of pressure on the melting temperature is considered. The mathematical analysis is made for different cases, depending on the sign of the three physical parameters. [ABSTRACT FROM AUTHOR]