Controllability of the semilinear Benjamin-Bona-Mahony equation

• Autorzy: Leiva H. , Merentes N. , Sanchez J. L.
• Języki publikacji: EN

Abstrakty

EN

In this paper we prove the interior approximate controllability of the following Generalized Semilinear Benjamin-Bona-Mahony type equation (BBM) with homogeneous Dirichlet boundary conditions [formula/wzor] where a ≥ 0 and b > 0 are constans, Ω is a domain in IR^N, ω is an open nonempty subset of Ω, 1_ω denotes the characteristic function of the set ω, the distributed control u belongs to L²(0, τ;L²(Ω)) and the nonlinear function ƒ:[0, τ] x IR x IR → IR is smooth enough and there are c, d, e ∈ IR, with c ≠ -1, ea + b > 0 such that [formula/wzor] where Q_r = [0, τ] x IR x IR. We prove that for all τ > 0 and any nonempty open subset ω of Ω the system the system is approximately controllable on [0, τ]. Moreover, we exhibit a sequence of controls steering the system from an initial state z₀ to an ε-neighborhood of the final state z₁ on time > 0. As a consequence of this result we obtain the interior approximate controllability of the semilinear heat equation by putting a = 0 and b = 1.

Słowa kluczowe

EN

interior controllability; semilinear BBM equation; strongly continuous semigroups

PL

sterowalność; równanie Benjamin-Bona-Mahony; mocno ciągłe półgrupy

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2012
• Tom: Vol. 35
• Strony: 39--51
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Leiva H.

• Departamento de Matemáticas, Universidad de Los Andes, Mérida 5101 – VENEZUELA

autor

Merentes N.

• Departamento de Matemáticas, Facultad de Ciencias, Universidad Central de Venezuela, Caracas 1051 VENEZUELA

autor

Sanchez J. L.

• Departamento de Matemáticas, Facultad de Ciencias, Universidad Central de Venezuela, Caracas 1051 VENEZUELA

Bibliografia

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