Publication

Existence for a Stationary Model of Binary Alloy Solidification

Jacques Rappaz, Linus Gasser
1995
Journal Articles

Abstract

A proof of existence is given for a stationary model of alloy solidification. The system is composed of heat equation, solute equation and Navier-Stokes equations. In rite latter Carman-Kozeny penalization of porous medium models the mushy zone. The problem is first regularized and a sequence of regularized solutions is built thanks to Leray-Schauder's fixed point Theorem. A solution is then extracted by compactness argument.

Official source

https://infoscience.epfl.ch/entities/publication/0288dd14-0ae2-4330-880d-b91d538241ac

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Jacques Rappaz, Linus Gasser
1995
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/0288dd14-0ae2-4330-880d-b91d538241ac

About this result

Related concepts (32)

Regularization (mathematics)

In mathematics, statistics, finance, computer science, particularly in machine learning and inverse problems, regularization is a process that changes the result answer to be "simpler". It is often used to obtain results for ill-posed problems or to prevent overfitting. Although regularization procedures can be divided in many ways, the following delineation is particularly helpful: Explicit regularization is regularization whenever one explicitly adds a term to the optimization problem.

Mathematical proof

A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning which establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning which establish "reasonable expectation".

Regularized least squares

Regularized least squares (RLS) is a family of methods for solving the least-squares problem while using regularization to further constrain the resulting solution. RLS is used for two main reasons. The first comes up when the number of variables in the linear system exceeds the number of observations. In such settings, the ordinary least-squares problem is ill-posed and is therefore impossible to fit because the associated optimization problem has infinitely many solutions.

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Existence for a Stationary Model of Binary Alloy Solidification

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