0577243 - MÚ 2025 RIV US eng J - Journal Article
Bhandari, Kuntal - Boyer, F.
Local exact controllability to the steady states of a parabolic system with coupled nonlinear boundary conditions.
Mathematical Control and Related Fields. Roč. 14, č. 3 (2024), s. 1086-1127. ISSN 2156-8472. E-ISSN 2156-8499
R&D Projects: GA ČR(CZ) GC22-08633J
Institutional support: RVO:67985840
Keywords : boundary controllability * fixed˦point argument * method of moments
OECD category: Pure mathematics
Impact factor: 1, year: 2023
Method of publishing: Limited access
https://doi.org/10.3934/mcrf.2023035

In this article, we study the boundary local exact controllability to any steady state of a one˦dimensional parabolic system with coupled nonlinear boundary conditions by means of only one control. The significant point is that the state components are interacting only at the boundary points with the assistance of some nonlinear terms. We consider two cases: either the control function is acting through a mixed nonlinear boundary condition on the first component or through a Neumann condition on the second component. The results are slightly different in the two cases. To study this problem, we first consider the associated linearized systems around the given steady state. The method of moments let us to prove its controllability and to obtain a suitable estimate of the control cost of the form MeM(T+ T1). To this end, we need to develop a precise spectral analysis of a non self˦adjoint operator. Thanks to those preliminary results, we can use the source term method developed in [29], followed by the Banach fixed point argument, to obtain the small˦time boundary local exact controllability to the steady state for the original system.
Permanent Link: https://hdl.handle.net/11104/0354803