Using sparse control methods to identify sources in linear diffusion-convection equations

被引：9
作者：
Casas, E. [1 ]
Kunisch, K. [2 ,3 ]
机构：
[1] Univ Cantabria, Dept Matemat Aplicada & Ciencias Comp, ETSI Ind & Telecomunicac, Santander 39005, Spain
[2] Karl Franzens Univ Graz, Inst Math & Sci Comp, Heinrichstr 36, A-8010 Graz, Austria
[3] Austrian Acad Sci, Radon Inst, A-4040 Linz, Austria
来源：
INVERSE PROBLEMS | 2019年 / 35卷 / 11期
基金：
欧盟地平线“2020”;
关键词：
measure controls; sparsity; parabolic equations; source identification; PARABOLIC CONTROL-PROBLEMS; ELLIPTIC CONTROL-PROBLEMS; MEASURE-SPACES; IDENTIFICATION;
D O I：
10.1088/1361-6420/ab331c
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Techniques from sparse control theory are proposed to approximate initial conditions for diffusion-convection equations. Existence and uniqueness of optimal controls are proven, and necessary and sufficient optimality conditions are derived. From these conditions the sparsity structure of the solutions is derived, which relates to identification of the sources to be reconstructed.
引用
收藏
页数：17
相关论文
共 20 条
  • [1] Brezies H., 2011, Functional Analysis. Sobolev Spaces and Partial Differential Equations, DOI [10.1007/978-0-387-70914-7, DOI 10.1007/978-0-387-70914-7]
  • [2] PARABOLIC CONTROL PROBLEMS IN SPACE-TIME MEASURE SPACES
    Casas, Eduardo
    Kunisch, Karl
    [J]. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2016, 22 (02) : 355 - 370
  • [3] PARABOLIC CONTROL PROBLEMS IN MEASURE SPACES WITH SPARSE SOLUTIONS
    Casas, Eduardo
    Clason, Christian
    Kunisch, Karl
    [J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2013, 51 (01) : 28 - 63
  • [4] APPROXIMATION OF ELLIPTIC CONTROL PROBLEMS IN MEASURE SPACES WITH SPARSE SOLUTIONS
    Casas, Eduardo
    Clason, Christian
    Kunisch, Karl
    [J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2012, 50 (04) : 1735 - 1752
  • [5] OPTIMAL CONTROL OF ELLIPTIC EQUATIONS WITH POSITIVE MEASURES
    Clason, Christian
    Schiela, Anton
    [J]. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2017, 23 (01) : 217 - 240
  • [6] A DUALITY-BASED APPROACH TO ELLIPTIC CONTROL PROBLEMS IN NON-REFLEXIVE BANACH SPACES
    Clason, Christian
    Kunisch, Karl
    [J]. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2011, 17 (01) : 243 - 266
  • [7] DiBenedetto E., 1986, Annali della Scuola Normale Superiore di Pisa-Classe di Scienze, V13, P487
  • [8] Identification of a point source in a linear advection-dispersion on-reaction equation: application to a pollution source problem
    El Badia, A
    Ha-Duong, T
    Hamdi, A
    [J]. INVERSE PROBLEMS, 2005, 21 (03) : 1121 - 1136
  • [9] ANALYTICITY OF SOLUTIONS TO PARABOLIC EVOLUTIONS AND APPLICATIONS
    Escauriaza, Luis
    Montaner, Santiago
    Zhang, Can
    [J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2017, 49 (05) : 4064 - 4092
  • [10] Friedman A., 1969, Partial differential equations
12