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http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-4f14a4f4-abf8-40eb-8f05-44140355d0d1

Czasopismo

Journal of Mathematics and Applications

Tytuł artykułu

Approximate controllability of the impulsive semilinear heat equation

Autorzy Leiva, H.  Merentes, N. 
Treść / Zawartość
Warianty tytułu
Języki publikacji EN
Abstrakty
EN In this paper we apply Rothe's Fixed Point Theorem to prove the interior approximate controllability of the following semilinear impulsive Heat Equation [...] where k = 1, 2, . . . , p, Ω is a bounded domain in [...] is an open nonempty subset of Ω, 1ω denotes the characteristic function of the set ω, the distributed control u belongs to [...]. Under this condition we prove the following statement: For all open nonempty subsets 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 nal state z1 at time τ > 0.
Słowa kluczowe
PL teoria punktu stałego   przestrzeń Banacha   równanie przewodnictwa ciepła   sterowalność   analiza funkcjonalna  
EN impulsive semilinear heat equation   approximate controllability   Rothe's fixed point theorem   functional analysis  
Wydawca Oficyna Wydawnicza Politechniki Rzeszowskiej
Czasopismo Journal of Mathematics and Applications
Rocznik 2015
Tom Vol. 38
Strony 85--104
Opis fizyczny Bibliogr. 24 poz., rys.
Twórcy
autor Leiva, H.
  • Universidad de los Andes, Facultad de Ciencias, Departamentode Matemática, Mérida 5101-Venezuela, hleiva@ula.ve
autor Merentes, N.
  • Universidad Central de Venezuela, Facultad de Ciencias, Departamento de Matemática, Caracas -Venezuela, nmerucv@gmail.com
Bibliografia
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[2] D. Barcenas, H. Leiva and Z. Sivoli, A Broad Class of Evolution Equations are Approximately Controllable, but Never Exactly Controllable. IMA J. Math. Control Inform. 22, no. 3 (2005), 310-320.
[3] H. Brezis, Analisis Funcional, Teoria y Applicaciones. Alianza Universitaria Textos, Masson, Paris, 1983. Ed. cast.: Alinza Editorial, S. A., Madrid, 1984.
[4] D. N. Chalishajar, Controllability of Impulsive Partial Neutral Funcional Differential Equation with Infinite Delay. Int. Journal of Math. Analysis, Vol. 5, 2011, No. 8, 369-380.
[5] Lizhen Chen and Gang Li, Approximate Controllability of Impulsive Differential Equations with Nonlocal Conditions. International Journal of Nonlinear Science, Vol.10(2010), No. 4, pp. 438-446.
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[10] C. Kesavan, Topics in: Functional Analysis and Applications. John Wiley and Sons, 1989.
[11] H. Leiva"Controllability of a System of Parabolic equation with non-diagonal diffusion matrix". IMA Journal of Mathematical Control and Information; Vol. 32, 2005, pp. 187-199.
[12] H. Leiva and Y. Quintana, "Interior Controllability of a Broad Class of Reaction Diffusion Equations", Mathematical Problems in Engineering, Vol. 2009, Article ID 708516, 8 pages, doi:10.1155/2009/708516.
[13] H. Leiva, N. Merentes and J.L. Sanchez,"Interior Controllability of the nD Semilinear Heat Equation". African Diaspora Journal of Mathematics, Special Vol. in Honor of Profs. C. Corduneanu, A. Fink, and S. Zaidman. Vol. 12, No. 2, pp. 1-12(2011).
[14] H. Leiva, N. Merentes and J. Sanchez "Approximate Controllability of Semilinear Reaction Diffusion" MATHEMATICAL CONTROL AND RALATED FIELDS, Vol. 2,No.2, June 2012.
[15] H. Leiva, N. Merentes and J. Sanchez "A Characterization of Semilinear Dense Range Operators and Applications", Abstract and Applied Analysis, Vol. 2013, Article ID 729093, 11 pages.
[16] H. Leiva, N. Merentes and J.L. Sanchez "Interior Controllability of the Benjamin-Bona-Mahony Equation". Journal of Mathematis and Applications, No 33,pp. 51-59 (2010).
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[18] M.H. Protter, Unique continuation for elliptic equations. Transaction of the American Mathematical Society, Vol. 95, No 1, Apr., 1960.
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[20] S. Selvi and M. Mallika Arjunan, Controllability Results for Impulsive Differential Systems with Finite Delay J. Nonlinear Sc. Appl. 5 (2012), 206-219.
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[24] E. Zuazua, Control of Partial Differential Equations and its Semi-Discrete Approximation. Discrete and Continuous Dynamical Systems, vol. 8, No. 2. April (2002), 469-513.
Kolekcja BazTech
Identyfikator YADDA bwmeta1.element.baztech-4f14a4f4-abf8-40eb-8f05-44140355d0d1
Identyfikatory
DOI 10.7862/rf.2015.8