Geodesic
On the solvability of boundary value problems for multidimensional parabolic equations of fourth order with nonlocal boundary condition of integral form
Matematičeskie zametki SVFU, Tome 23 (2016) no. 1, pp. 79-86 Cet article a éte moissonné depuis la source Math-Net.Ru

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We investigate solvability of the initial-boundary value problem for linear parabolic equations of fourth order with the boundary conditions connecting the values of solution or conormal the derivative of the solution with values of a certain integral operator from the solution. We prove the theorem of existence and uniqueness of regular solutions.
Keywords: parabolic equation of fourth order, Sobolev space, initial-boundary value problem, continuation method the parameter, a priori estimates, regular solutions. 
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N. S. Popov. On the solvability of boundary value problems for multidimensional parabolic equations of fourth order with nonlocal boundary condition of integral form. Matematičeskie zametki SVFU, Tome 23 (2016) no. 1, pp. 79-86. http://geodesic.mathdoc.fr/item/SVFU_2016_23_1_a7/

[1] Fridman A., “Monotone decay of solutions of parabolic equations with nonlocal boundary conditions”, Quart. Appl. Math., 44:3 (1986), 401–407 | DOI | MR

[2] Kozhanov A. I., “On resolvability of a regional problem with nonlocal boundary condition for the linear parabolic equations”, Vestn. Samar. Gos. Techn. Univ., 2004, no. 30, 63–69 | DOI

[3] Abdrahmanov A. M. and Kozhanov A. I., “A problem with a nonlocal boundary condition for one class of odd-order equations”, Russ Math., 51:1 (2007), 1–10 | DOI | MR | Zbl

[4] Kozhanov A. I. and Pulkina L. S., “On resolvability of regional problems with nonlocal boundary condition of an integrated kind for the multidimensional hyperbolic equations”, Differ. Equ., 42:9 (2006), 1116–1172

[5] Popov N. S., “On the solvability of boundary value problems for multidimensional pseudoparabolic equations with nonlocal boundary condition integral type”, Mat. Zamet. YaGU, 19:1 (2012), 82–95 | Zbl

[6] Popov N. S., “On the solvability of boundary value problems for higher-dimensional pseudohyperbolic equations with a nonlocal boundary condition in integral form”, Yak. Math. J., 21:2 (2014), 61–72 | Zbl

[7] Solonnikov V. A., “Boundary value problems for linear equations of general type”, Proc. Steklov Inst. Math., 83 (1965), 3–163

[8] Trenogin V. A., Functional analysis, Nauka, Moscow, 1980 | MR