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Identification of a source factor in a control problem for the heat equation with a boundary memory term
Author(s) -
Cavaterra Cecilia,
Guidetti Davide
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3397
Subject(s) - uniqueness , mathematics , bounded function , heat equation , operator (biology) , boundary (topology) , boundary value problem , identification (biology) , mathematical analysis , inverse problem , term (time) , control (management) , inverse , geometry , computer science , physics , biochemistry , chemistry , botany , repressor , quantum mechanics , artificial intelligence , biology , transcription factor , gene
We consider a material with thermal memory occupying a bounded region Ω with boundary Γ. The evolution of the temperature u ( t , x ) is described by an integrodifferential parabolic equation containing a heat source of the form f ( t ) z 0 ( x ). We formulate an initial and boundary value control problem based on a feedback device located on Γ and prescribed by means of a quite general memory operator. Assuming both u and the source factor f are unknown, we study the corresponding inverse and control problem on account of an additional information. We prove a result of existence and uniqueness of the solution ( u , f ). Copyright © 2015 John Wiley & Sons, Ltd.