Approximate controllability of semilinear strongly damped wave equation with impulses, delays, and nonlocal conditions
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Authors
Cosme Duque
- Departamento de Matematicas, Universidad de Los Andes, Merida 5101, Venezuela.
Jahnett Uzcategui
- Departamento de Matematicas, Universidad de Los Andes, Merida 5101, Venezuela.
Hugo Leiva
- School of Mathematical and Computational Sciences, University YachayTech, San Miguel de Urcuqui, Imbabura, Ecuador.
Oscar Camacho
- Departamento de Automatizacion y Control Industrial, Escuela Politecnica Nacional, Quito, Ecuador.
Abstract
In this paper, we prove that the interior approximate controllability of the linear strongly damped wave equation is not destroyed if we add impulses, nonlocal conditions, and a nonlinear perturbation with delay in the state. Specifically, we prove the interior approximate controllability of the semilinear strongly damped wave equation with impulses, delays, and nonlocal conditions. This is done by applying Roth's Fixed Point Theorem and the compactness of the semigroup generated by the linear uncontrolled system. Finally, we present some open problems and a possible general framework to study the controllability of impulsive semilinear second-order diffusion process in Hilbert spaces with delays and nonlocal conditions.
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ISRP Style
Cosme Duque, Jahnett Uzcategui, Hugo Leiva, Oscar Camacho, Approximate controllability of semilinear strongly damped wave equation with impulses, delays, and nonlocal conditions, Journal of Mathematics and Computer Science, 20 (2020), no. 2, 108--121
AMA Style
Duque Cosme, Uzcategui Jahnett, Leiva Hugo, Camacho Oscar, Approximate controllability of semilinear strongly damped wave equation with impulses, delays, and nonlocal conditions. J Math Comput SCI-JM. (2020); 20(2):108--121
Chicago/Turabian Style
Duque, Cosme, Uzcategui, Jahnett, Leiva, Hugo, Camacho, Oscar. "Approximate controllability of semilinear strongly damped wave equation with impulses, delays, and nonlocal conditions." Journal of Mathematics and Computer Science, 20, no. 2 (2020): 108--121
Keywords
- Interior approximate controllability
- impulsive semilinear strongly damped wave equation with delays and nonlocal conditions
- strongly continuous semigroups
- Rothe's fixed point theorem
MSC
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