A hyperbolic system and the cost of the null controllability for the Stokes system

被引：4
作者：
Chaves-Silva, F. W. [1 ]
机构：
[1] BCAM Basque Ctr Appl Math, Bilbao 48009, Basque Country, Spain
来源：
COMPUTATIONAL & APPLIED MATHEMATICS | 2015年 / 34卷 / 03期
关键词：
Stokes system; Null controllability; Cost of the controllability; Hyperbolic system with a pressure term; HEAT-EQUATIONS; SPATIAL DIMENSIONS; TRANSMUTATION; OBSERVABILITY; TIME;
D O I：
10.1007/s40314-014-0165-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is devoted to study the cost of the null controllability for the Stokes system. Using the control transmutation method, we show that the cost of driving the Stokes system to rest at time is of order e when , i.e., the same order of controllability as for the heat equation. For this to be possible, we prove a new exact controllability result for a hyperbolic system with a resistance term, which will be done under assumptions on the control region.
引用
收藏
页码：1057 / 1074
页数：18
相关论文
共 19 条
  • [1] OBSERVABILITY OF HEAT PROCESSES BY TRANSMUTATION WITHOUT GEOMETRIC RESTRICTIONS
    Ervedoza, Sylvain
    Zuazua, Enrique
    [J]. MATHEMATICAL CONTROL AND RELATED FIELDS, 2011, 1 (02) : 177 - 187
  • [2] Sharp Observability Estimates for Heat Equations
    Ervedoza, Sylvain
    Zuazua, Enrique
    [J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2011, 202 (03) : 975 - 1017
  • [3] Local exact controllability of the Navier-Stokes system
    Fernández-Cara, E
    Guerrero, S
    Imanuvilov, OY
    Puel, JP
    [J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2004, 83 (12): : 1501 - 1542
  • [4] Null and approximate controllability for weakly blowing up semilinear heat equations
    Fernández-Cara, E
    Zuazua, E
    [J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2000, 17 (05): : 583 - 616
  • [5] Fursikov A.V., 1996, Controllability of Evolution Equations
  • [6] Fundamental solutions of Stokes and Oseen problem in two spatial dimensions
    Guenther, Ronald B.
    Thomann, Enrique A.
    [J]. JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2007, 9 (04) : 489 - 505
  • [7] EXACT CONTROL OF THE HEAT-EQUATION
    LEBEAU, G
    ROBBIANO, L
    [J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1995, 20 (1-2) : 335 - 356
  • [8] Lions J.-L., 1988, RES APPL MATH, V8
  • [9] Lions JL, 1992, PITMAN RES NOTES MAT, V269, P196
  • [10] Geometric bounds on the growth rate of null-controllability cost for the heat equation in small time
    Miller, L
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 204 (01) : 202 - 226
12