A continuous dependence result for a nonstandard system of phase field equations. (20th June 2013)

• Record Type: Journal Article
• Authors: Colli, Pierluigi; Gilardi, Gianni; Krejčí, Pavel; Sprekels, Jürgen
• Is Part Of: Mathematical methods in the applied sciences. Volume 37:Number 9(2014:Jun. 15)
• Page Start: 1318
• Page End: 1324
• Publication Date: 2013-06-20
• Subjects: Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.2892
• Languages: English
• ISSNs: 0170-4214

Abstract

<abstract abstract-type="main" id="mma2892-abs-0001"> <title> <x xml:space="preserve">Abstract</x> </title> <p id="mma2892-para-0001">The present note deals with a nonstandard system of differential equations describing a two‐species phase segregation. This system naturally arises in the asymptotic analysis carried out recently by the same authors, as the diffusion coefficient in the equation governing the evolution of the order parameter tends to zero. In particular, an existence result has been proved for the limit system in a very general framework. On the contrary, uniqueness was shown by assuming a <italic>constant</italic> mobility coefficient. Here, we generalize this result and prove a continuous dependence property in the case that the mobility coefficient suitably depends on the chemical potential. Copyright © 2013 John Wiley &amp; Sons, Ltd.</p> </abstract>