A vanishing diffusion limit in a nonstandard system of phase field equations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F14%3A00428614" target="_blank" >RIV/67985840:_____/14:00428614 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.3934/eect.2014.3.257" target="_blank" >http://dx.doi.org/10.3934/eect.2014.3.257</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3934/eect.2014.3.257" target="_blank" >10.3934/eect.2014.3.257</a>

Result language
angličtina
Original language name
A vanishing diffusion limit in a nonstandard system of phase field equations
Original language description
We are concerned with a nonstandard phase field model of Cahn-Hilliard type. The model introduced by Podio-Guidugli (Ric. Mat. 2006) describes two-species phase segregation and consists of a system of two nonlinearly coupled PDEs. This paper investigatesthe asymptotic limit of the solutions to the initial-boundary value problems as the diffusion coefficient in the equation governing the evolution of the order parameter tends to zero. We prove that such a limit actually exists and solves the limit problem, which couples a nonlinear PDE of parabolic type with an ODE accounting for the phase dynamics. In the case of a constant diffusivity, we show uniqueness and improve the regularity of the solution.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GAP201%2F10%2F2315" target="_blank" >GAP201/10/2315: Mathematical modeling of Processes in Hysteretic Materials</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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