BEGIN:VCALENDAR
VERSION:2.0
METHOD:PUBLISH
CALSCALE:GREGORIAN
PRODID:-//WordPress - MECv5.17.2//EN
X-ORIGINAL-URL:https://matematica.unipv.it/
BEGIN:VEVENT
UID:MEC-4e8eaf897c638d519710b1691121f8cb@matematica.unipv.it
DTSTART:20200116T150000Z
DTEND:20200116T160000Z
DTSTAMP:20201026T102500Z
CREATED:20201026
LAST-MODIFIED:20210125
SUMMARY:Global Harnack Principle for a class of fast diffusion equations
DESCRIPTION:Nikita Simonov, Universidad Autonoma de Madrid \nAula Beltrami, Dipartimento di Matematica – Giovedì 16 Gennaio 2020 h.16:00\n \nAbstract. We study global properties of non-negative, integrable solutions to the Cauchy problem of the weighted fast diffusion equation $u_t = |x|^s div(|x|^{-r} \nabla u^m )$ with $(d − 2 − r)/(d − s) < m < 1$. The weights $|x|^s$ and $|x|^ {−r}$ , with $s < d$ and $s − 2 < r ≤ s(d − 2)/d$ can be both degenerate and singular and need not belong to the class A_2 , this range of parameters is optimal for the validity of a class of Caffarelli-Kohn-Nirenberg inequalities.\nWe characterize the largest class of data for which the so called Global Harnack Principle (GHP) holds\n(a global lower and upper bound in terms of suitable Barenblatt solutions). As a consequence of the GHP,\nwe prove convergence of the uniform relative error, namely $|(u − B)/B| \to 0$ as $t \to \infty$ uniformly in $R^d$,\nwhere B is a suitable Barenblatt solution. In the case with no weights ($s = r = 0$) and for a special\nclass of data, we give (almost) sharp rates of convergence to the Barenblatt profile in the $L^1$ and the $L^\infty$\ntopologies, in the radial case we give sharp rates.\nWe extend some of the results to non-negative, integrable solutions to the Cauchy problem of the\np-Laplace evolution equation $u_t = \Delta_p(u)$, where $\Delta_p(w) := div (|\nabla w|^(p−2) \nabla w)$, with$ 2d/(d + 1) < p < 2$.\nThe above results were obtained in collaboration with Prof. M. Bonforte and D. Stan.\n \n
URL:https://matematica.unipv.it/events/global-harnack-principle-for-a-class-of-fast-diffusion-equations/
ORGANIZER;CN=Nikita Simonov (Universidad Autonoma de Madrid):MAILTO:
CATEGORIES:Seminari di matematica applicata
LOCATION:Aula Beltrami
END:VEVENT
END:VCALENDAR