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On the solution set of the nonconvex sweeping process

100%

Gavioli A.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1999

tom 19

nr 1-2

45-65

We prove that the solutions of a sweeping process make up an $R_δ$-set under the following assumptions: the moving set C(t) has a lipschitzian retraction and, in the neighbourhood of each point x of its boundary, it can be seen as the epigraph of a lipschitzian function, in such a way that the diameter of the neighbourhood and the related Lipschitz constant do not depend on x and t. An application to the existence of periodic solutions is given.

Periodic solutions of evolution problem associated with moving convex sets

75%

Castaing C., Monteiro Marques M.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1995

tom 15

nr 2

99-127

This paper is concerned with periodic solutions for perturbations of the sweeping process introduced by J.J. Moreau in 1971. The perturbed equation has the form $-Du ∈ N_{C(t)}(u(t)) + f(t,u(t))$ where C is a T-periodic multifunction from [0,T] into the set of nonempty convex weakly compact subsets of a separable Hilbert space H, $N_{C(t)}(u(t))$ is the normal cone of C(t) at u(t), f:[0,T] × H∪H is a Carathéodory function and Du is the differential measure of the periodic BV solution u. Several existence results of periodic solutions for this differential inclusion are stated under various assumptions on the moving convex set C(t) and the perturbation f.

Ograniczanie wyników

2 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 Castaing C.

1 Gavioli A.

1 Monteiro Marques M.

1 1999

1 1995

Wyniki wyszukiwania

On the solution set of the nonconvex sweeping process

Periodic solutions of evolution problem associated with moving convex sets