Universal expansions in negative and complex bases.
Exact controllability of shells in minimal time
We prove an exact controllability result for thin cups using the Fourier method and recent improvements of Ingham type theorems, given in a previous paper [2].
An Ingham type proof for a two-grid observability theorem
Here, we prove the uniform observability of a two-grid method for the semi-discretization of the -wave equation for a time ; this time, if the observation is made in , is optimal and this result improves an earlier work of Negreanu and Zuazua [C. R. Acad. Sci. Paris Sér. I 338 (2004) 413–418]. Our proof follows an Ingham type approach.
General Gagliardo Inequality and Applications to Weighted Sobolev Spaces
In this paper we obtain a more general inequality with respect to a well known inequality due to Gagliardo (see [4], [5]). The inequality contained in [4], [5] has been extended to weighted spaces, obtained as cartesian product of measurable spaces. As application, we obtain a first order weighted Sobolev inequality. This generalize a previous result obtained in [2].
An Ingham type proof for a two-grid observability theorem
Here, we prove the uniform observability of a two-grid method for the semi-discretization of the -wave equation for a time ; this time, if the observation is made in , is optimal and this result improves an earlier work of Negreanu and Zuazua [ (2004) 413–418]. Our proof follows an Ingham type approach.
Well posedness and control of semilinear wave equations with iterated logarithms
Ingham type theorems and applications to control theory
Ingham [6] ha migliorato un risultato precedente di Wiener [23] sulle serie di Fourier non armoniche. Modificando la sua funzione di peso noi otteniamo risultati ottimali, migliorando precedenti teoremi di Kahane [9], Castro e Zuazua [3], Jaffard, Tucsnak e Zuazua [7] e di Ullrich [21]. Applichiamo poi questi risultati a problemi di osservabilità simultanea.
Homogenization of monotone systems of Hamilton-Jacobi equations
In this paper we study homogenization for a class of monotone systems of first-order time-dependent periodic Hamilton-Jacobi equations. We characterize the Hamiltonians of the limit problem by appropriate cell problems. Hence we show the uniform convergence of the solution of the oscillating systems to the bounded uniformly continuous solution of the homogenized system.
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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