"19"^^ . "A vanishing diffusion limit in a nonstandard system of phase field equations"@en . . . "2163-2480" . "nonstandard phase field system; nonlinear partial differential equations; asympotic limit"@en . "A vanishing diffusion limit in a nonstandard system of phase field equations"@en . "10.3934/eect.2014.3.257" . . . "Krej\u010D\u00ED, Pavel" . "RIV/67985840:_____/14:00428614!RIV15-GA0-67985840" . . "US - Spojen\u00E9 st\u00E1ty americk\u00E9" . "A vanishing diffusion limit in a nonstandard system of phase field equations" . . "2" . "3" . . . . "000344953200004" . "1"^^ . . "I, P(GAP201/10/2315)" . "4"^^ . "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." . "[AECE9A4BA897]" . "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 . "1264" . "Colli, P." . . . "RIV/67985840:_____/14:00428614" . . . "Evolution Equations and Control Theory" . . "Sprekels, J." . "A vanishing diffusion limit in a nonstandard system of phase field equations" . . "Gilardi, G." .