Article
On the uniform controllability for a family of non-viscous and viscous Burgers- α systems
Author/s | Araújo, Raul K.C.
Fernández Cara, Enrique Araujo de Souza, Diego |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2021-06-24 |
Deposit Date | 2022-07-01 |
Published in |
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Abstract | In this paper we study the global controllability of families of the so called non-viscous
and viscous Burgers- systems by using boundary and space independent distributed controls. In
these equations, the usual convective ... In this paper we study the global controllability of families of the so called non-viscous and viscous Burgers- systems by using boundary and space independent distributed controls. In these equations, the usual convective velocity of the Burgers equation is replaced by a regularized velocity, induced by a Helmholtz lter of characteristic wavelength . First, we prove a global exact controllability result (uniform with respect to ) for the non-viscous Burgers- system, using the return method and a xed-point argument. Then, the global uniform exact controllability to constant states is deduced for the viscous equations. To this purpose, we rst prove a local exact controllability property and, then, we establish a global approximate controllability result for smooth initial and target states. |
Citation | Araújo, R.K.C., Fernández Cara, E. y Araujo de Souza, D. (2021). On the uniform controllability for a family of non-viscous and viscous Burgers- α systems. ESAIM: Control, Optimisation and Calculus of Variations, 27, 78-1-78-26. |
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