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  • 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 investigates the 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.
  • 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 investigates the 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. (en)
Title
  • A vanishing diffusion limit in a nonstandard system of phase field equations
  • A vanishing diffusion limit in a nonstandard system of phase field equations (en)
skos:prefLabel
  • A vanishing diffusion limit in a nonstandard system of phase field equations
  • A vanishing diffusion limit in a nonstandard system of phase field equations (en)
skos:notation
  • RIV/67985840:_____/14:00428614!RIV15-GA0-67985840
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  • I, P(GAP201/10/2315)
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  • 1264
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  • RIV/67985840:_____/14:00428614
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  • nonstandard phase field system; nonlinear partial differential equations; asympotic limit (en)
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  • US - Spojené státy americké
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  • [AECE9A4BA897]
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  • Evolution Equations and Control Theory
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  • 3
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  • Colli, P.
  • Krejčí, Pavel
  • Sprekels, J.
  • Gilardi, G.
http://linked.open...ain/vavai/riv/wos
  • 000344953200004
issn
  • 2163-2480
number of pages
http://bibframe.org/vocab/doi
  • 10.3934/eect.2014.3.257
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