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Approximate Controllability of a Semilinear Heat Equation
Joint Authors
Sanchez, Jose Luis
Leiva, Hugo
Merentes, Nelson
Source
International Journal of Partial Differential Equations
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-11-03
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
We apply Rothe’s type fixed point theorem to prove the interior approximate controllability of the following semilinear heat equation: zt(t,x)=Δz(t,x)+1ωu(t,x)+f(t,z(t,x),u(t,x)) in (0,τ]×Ω,z=0, on (0,τ)×∂Ω,z(0,x)=z0(x), x∈Ω, where Ω is a bounded domain in ℝN (N≥1), z0∈L2(Ω), ω is an open nonempty subset of Ω, 1ω denotes the characteristic function of the set ω, the distributed control u belongs to L2(0,τ;L2(Ω)), and the nonlinear function f:[0,τ]×ℝ×ℝ→ℝ is smooth enough, and there are a,b,c∈ℝ, R>0 and 1/2≤β<1 such that |f(t,z,u)-az|≤c|u|β+b, for all u,z∈ ℝ,|u|,|z|≥R.
Under this condition, we prove the following statement: for all open nonempty subset ω of Ω, the system is approximately controllable on [0,τ].
Moreover, we could exhibit a sequence of controls steering the nonlinear system from an initial state z0 to an ϵ neighborhood of the final state z1 at time τ>0.
American Psychological Association (APA)
Leiva, Hugo& Merentes, Nelson& Sanchez, Jose Luis. 2013. Approximate Controllability of a Semilinear Heat Equation. International Journal of Partial Differential Equations،Vol. 2013, no. 2013, pp.1-7.
https://search.emarefa.net/detail/BIM-471087
Modern Language Association (MLA)
Leiva, Hugo…[et al.]. Approximate Controllability of a Semilinear Heat Equation. International Journal of Partial Differential Equations No. 2013 (2013), pp.1-7.
https://search.emarefa.net/detail/BIM-471087
American Medical Association (AMA)
Leiva, Hugo& Merentes, Nelson& Sanchez, Jose Luis. Approximate Controllability of a Semilinear Heat Equation. International Journal of Partial Differential Equations. 2013. Vol. 2013, no. 2013, pp.1-7.
https://search.emarefa.net/detail/BIM-471087
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-471087