Carleman inequality for a class of super strong degenerate parabolic operators and applications

Araújo, Bruno Sérgio and Demarque, Reginaldo and Viana, Luiz (2023) Carleman inequality for a class of super strong degenerate parabolic operators and applications. ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2023 (9). pp. 1-25. ISSN 1417-3875

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Abstract

In this paper, we present a new Carleman estimate for the adjoint equations associated to a class of super strong degenerate parabolic linear problems. Our approach considers a standard geometric imposition on the control domain, which can not be removed in general. Additionally, we also apply the aforementioned main inequality in order to investigate the null controllability of two nonlinear parabolic systems. The first application is concerned a global null controllability result obtained for some semilinear equations, relying on a fixed point argument. In the second one, a local null controllability for some equations with nonlocal terms is also achieved, by using an inverse function theorem.

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