Controllability of the semilinear parabolic equation governed by a multiplicative control in the reaction term: a qualitative approach. (English) Zbl 1041.93026

Khapalov, A. Y.

SIAM J. Control Optimization 41, No. 6, 1886-1900 (2003).

The author considers approximate controllability, i.e., tangibility of any desirable neighborhood of any desirable target state from any given initial state for the bilinear system defined by a Dirichlet boundary value problem with bilinear control: \[ \partial u/\partial t = \triangle u + vu - f(x,t,u, \nabla u),\quad (x,t)\in\Omega\times(0,T) \]
\[ u(x,t)=0,\quad (x,t)\in\partial\Omega\times(0,T),\quad u(x,0)=u_0(x)\in L^2(\Omega), \] where \(v\) is the control function.

Reviewer: Vladimir Răsvan (Craiova)

MSC:

93C20	Control/observation systems governed by partial differential equations
93B05	Controllability

Keywords:

parabolic equation; bilinear control; approximate controllability