Nonlocal cauchy problems and their controllability for semilinear differential inclusions with lower Scorza-Dragoni nonlinearities

Cardinali, Tiziana; Portigiani, Francesco; Rubbioni, Paola

doi:10.1007/s10587-011-0009-y

Cited by 10 publications

(2 citation statements)

References 21 publications

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“…Recent investigations of boundary value problems with nonlocal conditions similar to those appearing in this paper are contained in [4,5] and [7].…”

Section: Introductionmentioning

confidence: 99%

Nonsmooth feedback controls of nonlocal dispersal models

Malaguti

Rubbioni

2016

Nonlinearity

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The paper deals with a nonlocal diffusion equation which is a model for biological invasion and disease spread. A nonsmooth feedback control term is included and the existence of controlled dynamics is proved, satisfying different kinds of nonlocal condition. Jump discontinuities appear in the process. The existence of optimal control strategies is also shown, under suitably regular control functionals. The investigation makes use of techniques of multivalued analysis and is based on the degree theory for condensing operators in Hilbert spaces.

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“…Recent investigations of boundary value problems with nonlocal conditions similar to those appearing in this paper are contained in [4,5] and [7].…”

Section: Introductionmentioning

confidence: 99%

Nonsmooth feedback controls of nonlocal dispersal models

Malaguti

Rubbioni

2016

Nonlinearity

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“…See, e.g. [3,4,12,14,19,25] and the references therein. It is worth noting also that differential inclusions represent a useful and convenient tool for describing various optimal control problems (see, e.g.…”

Section: Introductionmentioning

confidence: 99%

Controllability for systems governed by semilinear evolution inclusions without compactness

Benedetti

Obukhovskiĭ

Taddei

2014

Nonlinear Differ. Equ. Appl.

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In this paper we study the controllability for a class of semilinear differential inclusions in Banach spaces. Since we assume the regularity of the nonlinear part with respect to the weak topology, we do not require the compactness of the evolution operator generated by the linear part. As well we are not posing any conditions on the multivalued nonlinearity expressed in terms of measures of noncompactness. We are considering the usual assumption on the controllability of the associated linear problem. Notice that, in infinite dimensional spaces, the above mentioned compactness of the evolution operator and linear controllability condition are in contradiction with each other. We suppose that the nonlinear term has convex, closed, bounded values and a weakly sequentially closed graph when restricted to its second argument. This regularity setting allows us to solve controllability problem under various growth conditions. As application, a controllability result for hyperbolic integro-differential equations and inclusions is obtained. In particular, we consider controllability of a system arising in a model of nonlocal spatial population dispersal and a system governed by the second order one-dimensional telegraph equation.

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Controllability of systems with a general nonlocal condition

Pinaud

Henrı́quez

2020

Journal of Differential Equations

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Nonlocal cauchy problems and their controllability for semilinear differential inclusions with lower Scorza-Dragoni nonlinearities

Cited by 10 publications

References 21 publications

Nonsmooth feedback controls of nonlocal dispersal models

Nonsmooth feedback controls of nonlocal dispersal models

Controllability for systems governed by semilinear evolution inclusions without compactness

Controllability of systems with a general nonlocal condition

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