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Controllability for parabolic equations with uniformly bounded nonlinear terms (1990)

Yamamoto, M. ; Park, J. Y.

Springer

Journal of optimization theory and applications 66 (1990), S. 515-532

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ISSN: 1573-2878

Keywords: Approximate controllability ; parabolic equations ; semilinear control systems ; uniformly bounded nonlinearities ; reachable sets

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract We consider a control system for a parabolic equation in a Banach space with uniformly bounded nonlinear termF, $$dz(t)/dt + Az(t) = F(t, z(t)) + Bf(t), t 〉 0.$$ Here,Bf(t) corresponds to a finite-dimensional control. We prove the equivalence of approximate controllability for the above nonlinear system and that for the linear system $$dz(t)/dt + Az(t) = Bf(t), t 〉 0.$$ Our method is based on results on approximate controllability for linear parabolic systems and estimates of solutions. A practical example is also given for a diffusion and reaction model.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00940936

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