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Pré-Publication, Document De Travail Année : 2023

Local null-controllability of a two-parabolic nonlinear system with coupled boundary conditions by a single Neumann control

Résumé

This article is concerned with the local boundary null-controllability of a 1d nonlinear system of two-parabolic equations with coupled boundary conditions by means of a single Neumann control. In the system, the nonlinear functions, appearing in the state equations, are considered as a combination of product, square and nonlocal nonlinearities. The control force is exerted on one of the two state components through a Neumann condition at the left end of the boundary while the other component simply satisfies the homogeneous Neumann condition at that point. On the other hand, the states are coupled at the right end of the boundary in terms of equality of their normal derivatives and a combined Robin-type condition. Upon linearization around the stationary point $(0, 0)$, we apply the so-called moments method to prove the global null-controllability of the associated linearized system with the explicit control cost $Ce^{C/T}$ as $T \to 0^+$. Then, we show the local null-controllability of the main system by employing the source term method developed in [27] followed by a Banach fixed point argument.
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Dates et versions

hal-04086267 , version 1 (01-05-2023)
hal-04086267 , version 2 (13-12-2023)

Identifiants

  • HAL Id : hal-04086267 , version 1

Citer

Kuntal Bhandari, Jiten Kumbhakar, Subrata Majumdar. Local null-controllability of a two-parabolic nonlinear system with coupled boundary conditions by a single Neumann control. 2023. ⟨hal-04086267v1⟩
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