Null controllability of semilinear degenerate parabolic equations in bounded domains.
Controllability of 1-D coupled degenerate parabolic equations.
On a maximum principle for elliptic systems with constant coefficients
Funzioni semiconcave, singolarità e pile di sabbia
La semiconcavità è una nozione che generalizza quella di concavità conservandone la maggior parte delle proprietà ma permettendo di ampliarne le applicazioni. Questa è una rassegna dei punti più salienti della teoria delle funzioni semiconcave, con particolare riguardo allo studio dei loro insiemi singolari. Come applicazione, si discuterà una formula di rappresentazione per la soluzione di un modello dinamico per la materia granulare.
Generalized gradient flow and singularities of the Riemannian distance function
Significant information about the topology of a bounded domain of a Riemannian manifold is encoded into the properties of the distance, , from the boundary of . We discuss recent results showing the invariance of the singular set of the distance function with respect to the generalized gradient flow of , as well as applications to homotopy equivalence.
A stability result for a class of nonlinear integrodifferential equations with L¹ kernels
We study second order nonlinear integro-differential equations in Hilbert spaces with weakly singular convolution kernels obtaining energy estimates for the solutions, uniform in t. Then we show that the solutions decay exponentially at ∞ in the energy norm. Finally, we apply these results to a problem in viscoelasticity.
Structural properties of singularities of semiconcave functions
Representation of equilibrium solutions to the table problem of growing sandpiles
In the dynamical theory of granular matter the so-called table problem consists in studying the evolution of a heap of matter poured continuously onto a bounded domain . The mathematical description of the table problem, at an equilibrium configuration, can be reduced to a boundary value problem for a system of partial differential equations. The analysis of such a system, also connected with other mathematical models such as the Monge–Kantorovich problem, is the object of this paper. Our main...
Singular dynamics for semiconcave functions
Interior sphere property of attainable sets and time optimal control problems
This paper studies the attainable set at time for the control system showing that, under suitable assumptions on , such a set satisfies a uniform interior sphere condition. The interior sphere property is then applied to recover a semiconcavity result for the value function of time optimal control problems with a general target, and to deduce C-regularity for boundaries of attainable sets.
Well posedness and control of semilinear wave equations with iterated logarithms
Null controllability of the heat equation in unbounded domains by a finite measure control region
Motivated by two recent works of Micu and Zuazua and Cabanillas, De Menezes and Zuazua, we study the null controllability of the heat equation in unbounded domains, typically or . Considering an unbounded and disconnected control region of the form , we prove two null controllability results: under some technical assumption on the control parts , we prove that every initial datum in some weighted space can be controlled to zero by usual control functions, and every initial datum in can...
Generation of analytic semi-groups in L2 for a class of second order degenerate elliptic operators
The vanishing viscosity method in infinite dimensions
The vanishing viscosity method is adapted to the infinite dimensional case, by showing that the value function of a deterministic optimal control problem can be approximated by the solutions of suitable parabolic equations in Hilbert spaces.
An existence and uniqueness result for Hamilton-Jacobi equations in Hilbert spaces
We prove an existence and uniqueness result for a class of Hamilton-Jacobi equations in Hilbert spaces.
The vanishing viscosity method in infinite dimensions
The vanishing viscosity method is adapted to the infinite dimensional case, by showing that the value function of a deterministic optimal control problem can be approximated by the solutions of suitable parabolic equations in Hilbert spaces.
An existence and uniqueness result for Hamilton-Jacobi equations in Hilbert spaces
We prove an existence and uniqueness result for a class of Hamilton-Jacobi equations in Hilbert spaces.
Null controllability of Grushin-type operators in dimension two
We study the null controllability of the parabolic equation associated with the Grushin-type operator , in the rectangle , under an additive control supported in an open subset of . We prove that the equation is null controllable in any positive time for and that there is no time for which it is null controllable for . In the transition regime and when is a strip ), a positive minimal time is required for null controllability. Our approach is based on the fact that, thanks to the particular...
Null controllability of the heat equation in unbounded domains by a finite measure control region
Motivated by two recent works of Micu and Zuazua and Cabanillas, De Menezes and Zuazua, we study the null controllability of the heat equation in unbounded domains, typically or . Considering an unbounded and disconnected control region of the form , we prove two null controllability results: under some technical assumption on the control parts , we prove that every initial datum in some weighted space can be controlled to zero by usual control functions, and every initial...
Well posedness and control of semilinear wave equations with iterated logarithms
Motivated by a classical work of Erdős we give rather precise necessary and sufficient growth conditions on the nonlinearity in a semilinear wave equation in order to have global existence for all initial data. Then we improve some former exact controllability theorems of Imanuvilov and Zuazua.
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