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Some remarks on the coincidence set for the Signorini problem

Benito Delgado de Miguel, Diaz Jesus Ildefonso

Opuscula Mathematica

2019

Vol. 39, no. 2

145--157

We study some properties of the coincidence set for the boundary Signorini problem, improving some results from previous works by the second author and collaborators. Among other new results, we show here that the convexity assumption on the domain made previously in the literature on the location of the coincidence set can be avoided under suitable alternative conditions on the data.

One-phase Stefan problem with temperature-dependent thermal conductivity and a boundary condition of Robin type

Briozzo A. C., Natale M. F.

Journal of Applied Analysis

2015

Vol. 21, nr 2

89--97

We study a one-phase Stefan problem for a semi-infinite material with temperature-dependent thermal conductivity with a boundary condition of Robin type at the fixed face x = 0. We obtain sufficient conditions for data in order to have a parametric representation of the solution of similarity type for t ≥ t0 > 0 with t0 an arbitrary positive time. This explicit solution is obtained through the unique solution of an integral equation with the time as a parameter.

The two-phase Hell-Shaw flow: construction of an exact solution

Malaikah K. R.

International Journal of Applied Mechanics and Engineering

2013

Vol. 18, no. 1

249--257

We consider a two-phase Hele-Shaw cell whether or not the gap thickness is time-dependent. We construct an exact solution in terms of the Schwarz function of the interface for the two-phase Hele-Shaw flow. The derivation is based upon the single-valued complex velocity potential instead of the multiple-valued complex potential. As a result, the construction is applicable to the case of the time-dependent gap. In addition, there is no need to introduce branch cuts in the computational domain. Furthermore, the interface evolution in a two-phase problem is closely linked to its counterpart in a one-phase problem.

Boundary optimal control problem for the phase-field transition system using fractional steps method

Moroşanu C.

Control and Cybernetics

2003

Vol. 32, no 1

5-32

In this paper we prove the convergence of an iterative scheme of fractional steps type for boundary optimal control problem which is governed by the phase-field transition system. The existence of an optimal control and necessary optimality conditions are given for approximating problem. A gradient type algorithm and numerical implementation of this algorithm are discussed.

W artykule dowodzi się zbieżności procedury iteracyjnej typu kroków ułamkowych dla zagadnienia sterowania optymalnego brzegiem w układzie pola ze zmianą fazy. Wykazano istnienie sterowania optymalnego i podano warunki konieczne optymalności dla zagadnienia aproksymującego. Rozpatrzono odpowiedni algorytm gradientowy oraz realizację numeryczną tego algorytmu.