Time nonlocal boundary value problem for a linearized phase field equations system
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 7 (2015) no. 3, pp. 10-15 Cet article a éte moissonné depuis la source Math-Net.Ru

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A boundary value problem with nonlocal time conditions is analyzed for a linearized quasi-steady system of phase field equations. Necessary and sufficient conditions are obtained for the existence and uniqueness of classical and generalized solutions.
Keywords: nonlocal problem; boundary value problem; system of phase field equations; classical solution; generalized solution.
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N. D. Ivanova; V. E. Fedorov. Time nonlocal boundary value problem for a linearized phase field equations system. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 7 (2015) no. 3, pp. 10-15. http://geodesic.mathdoc.fr/item/VYURM_2015_7_3_a1/

[1] Plotnikov P. I., Starovoytov V. N., “Stefan Problem with Surface Tension as the Limit of the Phase-field Model”, Differential Equations, 29:3 (1993), 395–404 (in Russ.) | MR | Zbl

[2] Plotnikov P. I., Klepacheva A. V., “Phase-field Equations and Gradient Flows of Marginal Functions”, Siberian Mathematical Journal, 42:3 (2001), 551–567 | DOI | MR | Zbl

[3] Fedorov V. E., “Degenerate strongly continuous semigroups of operators”, St. Petersburg Mathematical Journal, 12:3 (2001), 471–489 | MR | Zbl

[4] Tikhonov I. V., “Nonlocal problem with a “periodical” integral condition for a differential equation in Banach space”, Integralnye preobrazovaniya i spetsialnye funktsii, 4:1 (2004), 49–69 (in Russ.)

[5] Fedorov V. E., Ivanova N. D., Fedorova Yu. Yu., “On a time nonlocal problem for inhomogeneous evolution equations”, Siberian Mathematical Journal, 55:4 (2014), 721–733 | DOI | MR | Zbl