Identification of a source factor in a control problem for the heat equation with a boundary memory term | Zendy

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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.

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