A degenerate population system: Carleman estimates and controllability

Boutaayamou, Idriss; Fragnelli, Genni

doi:10.1016/j.na.2019.111742

Cited by 11 publications

(4 citation statements)

References 17 publications

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“…In [7] the problem is always in divergence form and k degenerates at an interior point x 0 and it belongs to C[0, 1] ∩ C 1 ([0, 1] \ {x 0 }); see also the recent paper [12], where the functions are less regular and both cases T < A and T > A are considered. The non divergence form is considered in [13], where k can degenerate at a one point of the boundary domain or in an interior point (for a cascade system we refer to [8]). We underline again that in all the previous papers, the memory kernel is zero.…”

Section: Systemmentioning

confidence: 99%

Null controllability for a degenerate population equation with memory

Allal¹,

Fragnelli²,

Salhi³

2021

Preprint

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In this paper we consider the null controllability for a population model depending on time, on space and on age. Moreover, the diffusion coefficient degenerate at the boundary of the space domain. The novelty of this paper is that for the first time we consider the presence of a memory term, which makes the computations more difficult. However, under a suitable condition on the kernel we deduce a null controllability result for the original problem via new Carleman estimates for the adjoint problem associated to a suitable nonhomogeneous parabolic equation.

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Section: Systemmentioning

confidence: 99%

Null controllability for a degenerate population equation with memory

Allal¹,

Fragnelli²,

Salhi³

2021

Preprint

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“…Recently, these estimates have been also studied for operators which are not uniformly parabolic. Indeed, as pointed out by several authors, many problems coming from Physics (see [31]), Biology (see [4], [5], [11], [17], [18], [19] and [27]) and Mathematical Finance (see [30]) are described by degenerate parabolic equations. In this framework, new Carleman estimates and null controllability properties have been established in [2], [9], [10], [20] and [33] for regular degenerate coefficients, in [5] and [21]- [25] for non smooth degenerate coefficients and in [14], [15], [16], [22], [23], [24], [26] and in [40] for degenerate and singular coefficients.…”

Section: Introductionmentioning

confidence: 99%

Boundary controllability for a degenerate wave equation in non divergence form with drift

Boutaayamou¹,

Fragnelli²,

Mugnai³

2021

Preprint

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We consider a degenerate wave equation with drift in presence of a leading operator which is not in divergence form. We provide some conditions for the boundary controllability of the associated Cauchy problem. * The author thanks ACRI Young Investigator Training Program 2018. † The author is a member of the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (IN-dAM) and a member of UMI "Modellistica Socio-Epidemiologica (MSE)". She is supported by the FFABR Fondo per il finanziamento delle attività base di ricerca 2017, by the INdAM -GNAMPA Project 2020 Problemi inversi e di controllo per equazioni di evoluzione e loro applicazioni, by Fondi di Ateneo 2017/18 of the University of Bari Problemi differenziali non linearii and by PRIN 2017-2019 Qualitative and quantitative aspects of nonlinear PDEs.‡ The author is a member of the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).

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“…The main results can be found in the books [1], [4], [15] and [35]. Some very recent achievements appear in [6], [17] and [21] to which we also refer for their bibliography.…”

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confidence: 98%

$ L^p $-exact controllability of partial differential equations with nonlocal terms

Malaguti

Perrotta

Taddei

2022

EECT

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<p style='text-indent:20px;'>The paper deals with the exact controllability of partial differential equations by linear controls. The discussion takes place in infinite dimensional state spaces since these equations are considered in their abstract formulation as semilinear equations. The linear parts are densely defined and generate strongly continuous semigroups. The nonlinear terms may also include a nonlocal part. The solutions satisfy nonlocal properties, which are possibly nonlinear. The states belong to Banach spaces with a Schauder basis and the results exploit topological methods. The novelty of this investigation is in the use of an approximation solvability method which involves a sequence of controllability problems in finite-dimensional spaces. The exact controllability of nonlocal solutions can be proved, with controls in <inline-formula><tex-math id="M2">\begin{document}$ L^p $\end{document}</tex-math></inline-formula> spaces, <inline-formula><tex-math id="M3">\begin{document}$ 1<p<\infty $\end{document}</tex-math></inline-formula>. The results apply to the study of the exact controllability for the transport equation in arbitrary Euclidean spaces and for the equation of the nonlinear wave equation.</p>

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A degenerate population system: Carleman estimates and controllability

Cited by 11 publications

References 17 publications

Null controllability for a degenerate population equation with memory

Null controllability for a degenerate population equation with memory

Boundary controllability for a degenerate wave equation in non divergence form with drift

$ L^p $-exact controllability of partial differential equations with nonlocal terms

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