A continuous dependence result for a nonstandard system of phase field equations

0430402 - MÚ 2015 RIV GB eng J - Journal Article
Colli, P. - Gilardi, G. - Krejčí, Pavel - Sprekels, J.
A continuous dependence result for a nonstandard system of phase field equations.
Mathematical Methods in the Applied Sciences. Roč. 37, č. 9 (2014), s. 1318-1324. ISSN 0170-4214. E-ISSN 1099-1476
R&D Projects: GA ČR GAP201/10/2315
Institutional support: RVO:67985840
Keywords : nonlinear differential equations * nonstandard phase field system * uniqueness and continuous dependence
Subject RIV: BA - General Mathematics
Impact factor: 0.918, year: 2014
http://onlinelibrary.wiley.com/doi/10.1002/mma.2892/abstract

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 constant 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.
Permanent Link: http://hdl.handle.net/11104/0235353