학술논문
Spike controls for elliptic and parabolic PDEs.
Document Type
Journal
Author
Casas, E. (E-SANTTC-CP) AMS Author Profile; Zuazua, E. (E-BCAM) AMS Author Profile
Source
Subject
35 Partial differential equations -- 35J Elliptic equations and systems
35J25Boundary value problems for second-order elliptic equations
35Partial differential equations -- 35K Parabolic equations and systems
35K20Initial-boundary value problems for second-order parabolic equations
93Systems theory; control -- 93C Control systems
93C20Systems governed by partial differential equations
35J25
35
35K20
93
93C20
Language
English
Abstract
The authors are interested in analyzing the issue of sparse control of elliptic and parabolic equations. They use measures of minimal norm to control these types of equations. They prove the ``sparsity'' of the optimal control. In the parabolic case, they prove that the solution of the optimization problem is a Borel measure supported in a set of Lebesgue measure zero. This is a well-written article which concludes with an excellent section of final comments and suggestions for open problems.