Controllability of the Semilinear Heat Equation with Impulses and Delay on the State

Hugo Leiva

Nonautonomous Dynamical Systems (2015)

  • Volume: 2, Issue: 1, page 52-62, electronic only
  • ISSN: 2353-0626

Abstract

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In this paper we prove the interior approximate controllability of the following Semilinear Heat Equation with Impulses and Delay [...] where Ω is a bounded domain in RN(N ≥ 1), φ : [−r, 0] × Ω → ℝ is a continuous function, ! is an open nonempty subset of Ω, 1ω denotes the characteristic function of the set ! and the distributed control u be- longs to L2([0, τ]; L2(Ω; )). Here r ≥ 0 is the delay and the nonlinear functions f , Ik : [0, τ] × ℝ × ℝ → ℝ are smooth enough, such that [...] Under this condition we prove the following statement: For all open nonempty subset ! of Ω the system is approximately controllable on [0, τ], for all τ > 0.

How to cite

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Hugo Leiva. "Controllability of the Semilinear Heat Equation with Impulses and Delay on the State." Nonautonomous Dynamical Systems 2.1 (2015): 52-62, electronic only. <http://eudml.org/doc/276524>.

@article{HugoLeiva2015,
abstract = {In this paper we prove the interior approximate controllability of the following Semilinear Heat Equation with Impulses and Delay [...] where Ω is a bounded domain in RN(N ≥ 1), φ : [−r, 0] × Ω → ℝ is a continuous function, ! is an open nonempty subset of Ω, 1ω denotes the characteristic function of the set ! and the distributed control u be- longs to L2([0, τ]; L2(Ω; )). Here r ≥ 0 is the delay and the nonlinear functions f , Ik : [0, τ] × ℝ × ℝ → ℝ are smooth enough, such that [...] Under this condition we prove the following statement: For all open nonempty subset ! of Ω the system is approximately controllable on [0, τ], for all τ > 0.},
author = {Hugo Leiva},
journal = {Nonautonomous Dynamical Systems},
keywords = {interior approximate controllability; semilinear heat equation with impulses and delay; strongly continuous semigroup; strongly continuous semigroup},
language = {eng},
number = {1},
pages = {52-62, electronic only},
title = {Controllability of the Semilinear Heat Equation with Impulses and Delay on the State},
url = {http://eudml.org/doc/276524},
volume = {2},
year = {2015},
}

TY - JOUR
AU - Hugo Leiva
TI - Controllability of the Semilinear Heat Equation with Impulses and Delay on the State
JO - Nonautonomous Dynamical Systems
PY - 2015
VL - 2
IS - 1
SP - 52
EP - 62, electronic only
AB - In this paper we prove the interior approximate controllability of the following Semilinear Heat Equation with Impulses and Delay [...] where Ω is a bounded domain in RN(N ≥ 1), φ : [−r, 0] × Ω → ℝ is a continuous function, ! is an open nonempty subset of Ω, 1ω denotes the characteristic function of the set ! and the distributed control u be- longs to L2([0, τ]; L2(Ω; )). Here r ≥ 0 is the delay and the nonlinear functions f , Ik : [0, τ] × ℝ × ℝ → ℝ are smooth enough, such that [...] Under this condition we prove the following statement: For all open nonempty subset ! of Ω the system is approximately controllable on [0, τ], for all τ > 0.
LA - eng
KW - interior approximate controllability; semilinear heat equation with impulses and delay; strongly continuous semigroup; strongly continuous semigroup
UR - http://eudml.org/doc/276524
ER -

References

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