Gradient Optimal Control of the Bilinear Reaction–Diffusion Equation
In this chapter, we study a problem of gradient optimal control for a bilinear reaction–diffusion equation evolving in a spatial domain Ω⊂Rn using distributed and bounded controls. Then, we minimize a functional constituted of the deviation between the desired gradient and the reached one and the en...
Guardado en:
| Autores principales: | , |
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| Formato: | Capítulo de libro |
| Lenguaje: | inglés |
| Publicado: |
IntechOpen
2021
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| Materias: | |
| Acceso en línea: | https://www.intechopen.com/chapters/75398 |
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| Sumario: | In this chapter, we study a problem of gradient optimal control for a bilinear reaction–diffusion equation evolving in a spatial domain Ω⊂Rn using distributed and bounded controls. Then, we minimize a functional constituted of the deviation between the desired gradient and the reached one and the energy term. We prove the existence of an optimal control solution of the minimization problem. Then this control is characterized as solution to an optimality system. Moreover, we discuss two special cases of controls: the ones are time dependent, and the others are space dependent. A numerical approach is given and successfully illustrated by simulations. |
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| ISBN: | 978-1-83968-656-6 |
| DOI: | 10.5772/intechopen.96041 |