in revised form 18.01.2019, accepted 06.03.2019 This article deals with the heat equation @tu− @2xu = f in D; D = { (t; x) ∈ R2 2 a < t < b; (t) < x < +∞} with the function satisfying some conditions and the problem is supplemented with boundary conditions...
and preliminaries This work is devoted to the analysis of the following one-dimensional second order parabolic problem  @tu− @2xu = f ∈ a2(Ω∞); @xu+ �u|Γ) = 0; @xu|Γ2 = 0; (1) where a2(Ω∞) stands for the space of square-integrable functions on Ω...

) Khach82@rambler.ru c⃝ Siberian Federal University. All rights reserved – 416 – A.Kh.Khachatryan, Kh.A Khachatryan, Tigran H.Sardaryan On Solvability of one Class of Nonlinear ... We assume that there exists a number >0, such that ♯ (x;u) u 0 (x;u...
) > 0; (x;u) 2 R+ R+: (7) Problem (1)–(2) has direct application in econometrics, namely, in the theory of income distribution in one product economics (see. [1–4]). Unknown function f (x) plays a role of distribution density, i.e. f (x)dx is a number...

to other components) by analogy with [9, 10]. ( ) ( ) ( ) ( ) ( ) 3 3 2 2 2 2 2 ,1 )(2 1)( , ),( )( ,)(, X tXW R XEI RX XIEtXN X tXUXEF X tXU X XFE t tXUXm X X Д K ∂ ∂+⋅∂ ∂+= =∂ ∂−∂ ∂⋅∂ ∂−∂ ∂ ; (5...
to other components) by analogy with [9, 10]. ( ) ( ) ( ) ( ) ( ) 3 3 2 2 2 2 2 ,1 )(2 1)( , ),( )( ,)(, X tXW R XEI RX XIEtXN X tXUXEF X tXU X XFE t tXUXm X X Д K ∂ ∂+⋅∂ ∂+= =∂ ∂−∂ ∂⋅∂ ∂−∂ ∂ ; (5...

nad4_exon4; scaffold_16; 170398..170484. Работа выполнена в лаборатории лесной геномики СФУ.

,† Xiaoyong Wei,‡ Yujun Feng,‡ Ran Xu,‡ and Tian Zhao‡ †Kirensky Institute of Physics & Siberian Federal University, Krasnoyarsk, 660036, Russia ‡Electronic Materials Research Laboratory & Intl. Center for Dielectric Research, Xi’an, 710049, China †vtyurin...
at the transition point that supposes considerable inter mode interactions via dampings. References 1M. E. Lines and A. M. Glass, Principles and Application of Ferroelectrics and Related Materials (Clarendon Press, Oxford, 1977). 2Z. Xu, Y.J. Feng, S.G. Zheng...

. Oreshonkov,† Xiaoyong Wei,‡ Yujun Feng,‡ Ran Xu,‡ and Tian Zhao‡ †Kirensky Institute of Physics & Siberian Federal University, Krasnoyarsk, 660036, Russia ‡Electronic Materials Research Laboratory & Intl. Center for Dielectric Research, Xi’an, 710049...
(Clarendon Press, Oxford, 1977). 2Z. Xu, Y.J. Feng, S.G. Zheng, A. Jin, F. L. Wang, and X. Yao, J. Appl. Phys. 92 (5), 2663 (2002). 3W. D. Dong, J. C. Valadez, J. A. Gallagher, H. R. Jo, R. Sahul, W. Hackenberger, and C. S. Lynch, J. Appl. Phys. 117...

boundary-value problems for equation systems with small parame- ters [8,9]. 1. Problem formulation We consider the boundary-value problem ∂u(t,x,y) ∂t = λ∆xu(t,x,y) +µ(t,y)f(t,x,y), (1) u(0,x,y) = u0(x,y), (2) u(t,x,y)|x∈∂Ω = 0, (3) u(t,x,y)|x=y = φ...
for the Cauchy problem ∂u(t,x,y) ∂t = λ∆xu(t,x,y) +µ(t,y)f ∗(t,x,y), (12) u(0,x,y) = u∗0(x,y), (13) u(t,x,y)|x=y = φ(t,y), (14) for t∈ [0,T], x∈ Rn, y ∈D ⊂ Rn. After substitution x = y, y ∈D to (12) one can find µ(t,y): µ(t,y) = 1f∗(t,y,y) (φt(t,y)−λ∆xu(t,y,y)), y...

relaxation and phase transition behavior of (1- x)Pb(Zn1/3Nb2/3)O3-xBaTiO3 binary solid solutions Qiang Gao, Qingyuan Hu, Li Jin, M.V. Gorev, D.S. Chezganov, E.O. Vlasov, Huarong Zeng, Luyang Zhao, Yu Cui, Zhuo Xu, Xiaoyong Wei aElectronic Materials Research...

) + ‖∂tw‖2L2(D) + 2∑ j=1 ∥∥∂jxw∥∥2L2(D) . We consider the problem: to find a function u ∈ H1,2(D) that satisfies the equation ∂tu− x(t)∂2xu = f a.e. on D (1.1) and the boundary conditions u|Γ1 = ∂xu+ β2u|Γ2 = 0P (1.2) where f ∈ a2(D) and the coefficient x...
> 0. Fig. 1. The unbounded non-rectangular domain D Problem (1.1)–(1.2) modelizes, for instance, the lateral diffusion of a pollutant in a flow of a river with variable width. Note that the Robin type condition ∂xu+ β2u|Γ2 = 0P means for instance...

терминологию и обозначения, приня- тые в [6,7]. Пусть задан (n,m)-гиперграф H = (X,U), где X = {x1,...,xn} emdash.cyr конечное множество вершин и U = {u1,...,um} emdash.cyr конечное семейство ребер гиперграфа, при этом n = |X| greaterorequalslant 1,m = |U...
| greaterorequalslant 1 и всякое ребро гиперграфа emdash.cyr некоторое подмножество множества X. Пусть U(x) emdash.cyr множество ребер, инцидентных в H вершине x ∈ X, а X(u) – множество всех вершин, инцидентных ребру u ∈ U. Тогда число |U(x)| определяет степень вершины...