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Controllability of a class of heat equations with memory in one dimension
- Source :
- Mathematical Methods in the Applied Sciences. 40:3066-3078
- Publication Year :
- 2016
- Publisher :
- Wiley, 2016.
-
Abstract
- This paper addresses a study of the controllability for a class of heat equations with memory in one spacial dimension. Unlike the classical heat equation, a heat equation with memory in general is not null controllable. There always exists a set of initial values such that the property of the null controllability fails. Also, one does not know whether there are nontrivial initial values, which can be driven to zero with a boundary control. In this paper, we give a characterization of the set of such nontrivial initial values. On the other hand, if a moving control is imposed on this system with memory, we prove the null controllability of it in a suitable state space for any initial value. Copyright © 2016 John Wiley & Sons, Ltd.
- Subjects :
- 0209 industrial biotechnology
General Mathematics
010102 general mathematics
Null (mathematics)
Mathematical analysis
General Engineering
Boundary (topology)
02 engineering and technology
01 natural sciences
Volterra integral equation
Controllability
symbols.namesake
020901 industrial engineering & automation
Dimension (vector space)
symbols
Initial value problem
State space
Heat equation
0101 mathematics
Mathematics
Subjects
Details
- ISSN :
- 01704214
- Volume :
- 40
- Database :
- OpenAIRE
- Journal :
- Mathematical Methods in the Applied Sciences
- Accession number :
- edsair.doi...........cd3559d5de90570074218942895e3645