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Controllability properties of the reaction diffusion equation

29 pages
Controllability properties of the reaction-diffusion equation governed by multiplicative controls A.Y. Khapalov Department of Mathematics Washington State University, Pullman, WA 99164-3113 USA 1

  • control supports

  • results include

  • properties both

  • reaction-diffusion equation

  • st problem

  • approximate controllability

  • wave equations

  • controllability properties

  • schrodinger equation


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Controllability properties of the reaction-diffusion equation
Washington
governed by multiplicative controls
A.Y. Khapalov
Department of Mathematics
State
University,
Pullman,
1
WA
99164-3113
USA
Abstract
We discuss several recent results relative to the global approximate con-trollability properties of the one dimensional reaction-diffusion equation governed by a control that enters the system equation as a coefficient in the reaction term. The traditional (linear operator) controllability meth-ods based on the duality pairing do not apply in this highly nonlinear setting. Instead, we focus on the qualitative study of the diffusion and reaction parts of the evolution process at hand.
The 1-st problem we discuss is the case when both the initial and desirable target states can change sign at no more than finitely many isolated points.This is a joint work with Piermarco Cannarsa.
The 2-nd problem we discuss is the case when the multiplicative control acts within a proper subset of the system’s space domain. The main results include approximate controllability properties both for the static and mobile control supports.This is a joint work with Luis Alberto Fernandez.
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