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November 27, 2017

  

Monday, November 27, 2017

(Cancelled) Seminars in Research in Biochemistry and Molecular Biology
12:00 PM - 1:00 PM

Bloomberg School of Public Health

Seminars in Research in Biochemistry and Molecular Biology
Stopping the Kosovar War - Protecting the Young Nation
12:00 PM - 1:20 PM

Bloomberg School of Public Health

Center for Humanitarian Health
International Health

Carlo Scognamiglio Pasini, Minister of Defense, Italy (1998 – 2000)
Risk Management of Emergency Service Vehicle Crashes in the U.S. Fire Service
12:10 PM - 1:20 PM

Graduate Seminar in Injury Research and Policy

Keshia Pollack Porter, PhD, MPH
Professor, Director – Institute for Health and Social Policy, Associate Director – Johns Hopkins Center for Injury Research and Policy, Department of Health Policy and Management, Johns Hopkins Bloomberg School of Public Health

Hampton House Room 250
4th Health Sector Program of Bangladesh
12:30 PM - 1:30 PM

International Center for Maternal and Newborn Health Special Seminar: 4th Health Sector Program of Bangladesh
A. E. Md. Muhiuddin Osmani MBBS, FCPS
Joint Chief, Bangladesh Ministry of Health and Family Welfare
Anna Baetjer Room (W1030)
Biostatistics Help: Faculty, Staff, Pre and Post Doc Walk-In Clinic
1:30 PM - 2:30 PM

Biostatistics consulting is available to all Johns Hopkins University faculty, staff, pre and post docs conducting clinical and translational research. 1:30 – 2:30 PM Wolfe Street Building Room: E3142
Matteo Bonforte "Nonlinear and Nonlocal Degenerate Diffusions on Bounded Domains."
4:00 PM - 5:00 PM

Homewood

Speaker: Matteo Bonforte, (U Autonoma de Madrid) Abstract: We investigate quantitative properties of nonnegative solutions $u(t,x)\ge 0$ to the nonlinear fractional diffusion equation, $\partial_t u + \mathcal{L} F(u)=0$ posed in a bounded domain, $x\in\Omega\subset \mathbb{R}^N$, with appropriate homogeneous Dirichlet boundary conditions. As $\mathcal{L}$ we can use a quite general class of linear operators that includes the three most common versions of the fractional Laplacian $(-\Delta)^s$, $01$. First we present some result about sharp boundary behaviour and regularity for the associated stationary elliptic problem (semilinear). Next, we will shortly present some recent results about existence, uniqueness and a priori estimates for a quite large class of very weak solutions, that we call weak dual solutions. We will devote special attention to the regularity theory: decay and positivity, boundary behavior, Harnack inequalities, interior and boundary regularity, and (sharp) asymptotic behavior. All this is done in a quantitative way, based on sharp a priori estimates. Although our focus is on the fractional models, our techniques cover also the local case s = 1 and provide new results even in this setting. A surprising instance of this problem is the possible presence of nonmatching powers for the boundary behavior: for instance, when $\mathcal{L}=(-\Delta)^s$ is a spectral power of the Dirichlet Laplacian inside a smooth domain, we can prove that, whenever $2s > 1 - 1/m$, solutions behave as $dist^{1/m}$ near the boundary; on the other hand, when $2s \le 1 - 1/m$, different solutions may exhibit different boundary behaviors even for large times. This unexpected phenomenon is a completely new feature of the nonlocal nonlinear structure of this model, and it is not present in the semilinear elliptic case, for which we will shortly present the most recent results. The above results are contained on a series of recent papers in collaboration with A. Figalli, Y. Sire, X. Ros-Oton and J. L. Vazquez.

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