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# Documents  35Q53 | enregistrements trouvés : 4

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## Post-edited  Pathwise regularisation by noise in PDEs Gubinelli, Massimiliano (Auteur de la Conférence) | CIRM (Editeur )

We discuss some examples of the "good" effects of "very bad", "irregular" functions. In particular we will look at non-linear differential (partial or ordinary) equations perturbed by noise. By defining a suitable notion of "irregular" noise we are able to show, in a quantitative way, that the more the noise is irregular the more the properties of the equation are better. Some examples includes: ODE perturbed by additive noise, linear stochastic transport equations and non-linear modulated dispersive PDEs. It is possible to show that the sample paths of Brownian motion or fractional Brownian motion and related processes have almost surely this kind of irregularity. (joint work with R. Catellier and K. Chouk) We discuss some examples of the "good" effects of "very bad", "irregular" functions. In particular we will look at non-linear differential (partial or ordinary) equations perturbed by noise. By defining a suitable notion of "irregular" noise we are able to show, in a quantitative way, that the more the noise is irregular the more the properties of the equation are better. Some examples includes: ODE perturbed by additive noise, linear ...

## Multi angle  Linear transformations for the stabilization of nonlinear partial differential equations Coron, Jean-Michel (Auteur de la Conférence) | CIRM (Editeur )

We start by presenting some results on the stabilization, rapid or in finite time, of control systems modeled by means of ordinary differential equations. We study the interest and the limitation of the damping method for the stabilization of control systems. We then describe methods to transform a given linear control system into new ones for which the rapid stabilization is easy to get. As an application of these methods we show how to get rapid stabilization for Korteweg-de Vries equations and how to stabilize in finite time $1-D$ parabolic linear equations by means of periodic time-varying feedback laws. We start by presenting some results on the stabilization, rapid or in finite time, of control systems modeled by means of ordinary differential equations. We study the interest and the limitation of the damping method for the stabilization of control systems. We then describe methods to transform a given linear control system into new ones for which the rapid stabilization is easy to get. As an application of these methods we show how to get ...

## Multi angle  Singularity formation in semilinear dispersing / parabolic problem Raphaël, Pierre (Auteur de la Conférence) | CIRM (Editeur )

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