Publication

Existence of solutions to a phase-field model for the isothermal solidification process of a binary alloy

Jacques Rappaz
2000
Journal Articles

Abstract

We investigate the well-posedness of a phase-field model for the isothermal solidification of a binary alloy due to Warren-Boettinger [12]. Existence of weak solution as well as regularity and uniqueness results are established under Lipschitz and boundedness assumptions for the non-linearities. A maximum principle holds that guarantees the existence of a solution under physical assumptions on the non-linearities. Copyright (C) 2000 John Wiley & Sons, Ltd.

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Jacques Rappaz
2000
Journal Articles

Abstract

Official source

Related concepts (27)

Aqueous solution

An aqueous solution is a solution in which the solvent is water. It is mostly shown in chemical equations by appending (aq) to the relevant chemical formula. For example, a solution of table salt, or sodium chloride (NaCl), in water would be represented as . The word aqueous (which comes from aqua) means pertaining to, related to, similar to, or dissolved in, water. As water is an excellent solvent and is also naturally abundant, it is a ubiquitous solvent in chemistry.

Aluminium alloy

An aluminium alloy (or aluminum alloy; see spelling differences) is an alloy in which aluminium (Al) is the predominant metal. The typical alloying elements are copper, magnesium, manganese, silicon, tin, nickel and zinc. There are two principal classifications, namely casting alloys and wrought alloys, both of which are further subdivided into the categories heat-treatable and non-heat-treatable. About 85% of aluminium is used for wrought products, for example rolled plate, foils and extrusions.

Alloy

An alloy is a mixture of chemical elements of which at least one is a metal. Unlike chemical compounds with metallic bases, an alloy will retain all the properties of a metal in the resulting material, such as electrical conductivity, ductility, opacity, and luster, but may have properties that differ from those of the pure metals, such as increased strength or hardness. In some cases, an alloy may reduce the overall cost of the material while preserving important properties.