Smooth Solution of the First Initial-Boundary Value Problem for Parabolic Systems in a Semibounded Domain with Nonsmooth Lateral Boundary on the Plane

被引：1
作者：
Fedorov, K. D. [1 ,2 ]
机构：
[1] Lomonosov Moscow State Univ, Moscow 119991, Russia
[2] Moscow Ctr Fundamental & Appl Math, Moscow 119991, Russia
来源：
DIFFERENTIAL EQUATIONS | 2022年 / 58卷 / 10期
关键词：
D O I：
10.1134/S00122661220100093
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider the first initial-boundary value problem for homogeneous second-order parabolic systems with Dini continuous coefficients in a semibounded domain omega on the plane with a curvilinear lateral boundary that is nonsmooth at t=0 . The existence of a solution of this problem in the class C-x,t(2,1)((omega) over bar) is proved by the method of boundary integral equations.
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页码：1396 / 1409
页数：14
相关论文
共 13 条
[1]   Uniqueness of Solutions of Initial-Boundary Value Problems for Parabolic Systems with Dini-Continuous Coefficients in Domains on the Plane [J].
Baderko, E. A. ;
Sakharov, S. I. .
DOKLADY MATHEMATICS, 2022, 105 (02) :71-74
[2]   Dirichlet problem for parabolic systems with Dini continuous coefficients [J].
Baderko, E. A. ;
Cherepova, M. F. .
APPLICABLE ANALYSIS, 2021, 100 (13) :2900-2910
[3]   The first boundary value problem for parabolic systems in plane domains with nonsmooth lateral boundaries [J].
Baderko, E. A. ;
Cherepova, M. F. .
DOKLADY MATHEMATICS, 2014, 90 (02) :573-575
[4]  
BADERKO EA, 1983, DIFF EQUAT+, V19, P6
[5]  
Dzyadyk VK, 1977, VVEDENIE TEORIYU RAV
[6]   On the First Initial-Boundary Value Problem for a Model Parabolic System in a Domain with Curvilinear Lateral Boundaries [J].
Fedorov, K. D. .
DIFFERENTIAL EQUATIONS, 2021, 57 (12) :1598-1609
[7]  
Friedman A., 1964, Partial differential equations of parabolic type, Englewood Cliffs
[8]  
Kamynin L.I., 1970, SIBERIAN MATH J+, V11, P1017
[9]  
LADYzHENSKAYA A ..., 1968, LINEAR QUASILINEAR E
[10]  
Petrovskii I. G., 1938, Byull. Mosk. Gos. Univ. Ser. A: Mat. Mekh, V1, P1
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