We consider the one-dimensional degenerate parabolic equation u< sub> t-(x< sup> α u<
sub> x)< sub> x= 0 x∊(0, 1), t∊(0, T), controlled by a boundary force acting at the …

We prove local exact controllability in arbitrarily short time of the two-dimensional
incompressible Euler equation with free surface, in the case with surface tension. This …

In this paper, we prove explicit lower bounds for the cost of fast boundary controls for a class
of linear equations of parabolic or dispersive type involving the spectral fractional Laplace …

We consider the typical one-dimensional strongly degenerate parabolic operator Pu= ut−(x
α ux) x with 0< x< ℓ and α∈(0, 2), controlled either by a boundary control acting at x= ℓ, or by …

In this paper, we study the quantitative analyticity and observability inequality for solutions of
fractional order parabolic equations with space-time dependent potentials in ℝ n. We first …

For α∈(0,2) we study the null controllability of the parabolic operator Pu=u_t-(|x|^αu_x)_x -
1<x<1), which degenerates at the interior point x=0 for locally distributed controls acting only …

The general goal of this work is to obtain upper and lower bounds for the $ L^ 2$-norm of
biorthogonal families to complex exponential functions associated to sequences …

In this paper, we consider the following degenerate/singular parabolic equation $$ u_t-
(x^\alpha u_ {x}) _x-\frac {\mu}{x^{2-\alpha}} u= 0,\qquad x\in (0, 1),\t\in (0, T), $$ where …

In this article, we revisit a result by A. Koenig concerning the non-controllability of the half-
heat equation posed on R, with a control domain that is an open set whose exterior contains …

This paper is devoted to the stabilization of the two-dimensional water-wave equations with
surface tension through an external pressure acting on a small part of the free surface. It is …