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- Title
Identification of a source factor in a control problem for the heat equation with a boundarymemory term.
- Authors
Cavaterra, Cecilia; Guidetti, Davide
- Abstract
We consider a material with thermal memory occupying a bounded region O with boundary G. The evolution of the temperature u(t,x) is described by an integrodifferential parabolic equation containing a heat source of the form f(t)z0(x). We formulate an initial and boundary value control problem based on a feedback device located on G 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).
- Subjects
INTEGRO-differential equations; PARABOLIC differential equations; BOUNDARY value problems; PARTIAL differential equations; INVERSE problems; UNIQUENESS (Mathematics)
- Publication
Mathematical Methods in the Applied Sciences, 2015, Vol 38, Issue 18, p4818
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.3397