Difusión no lineal en Madrid

Seminario conjunto de las universidades: UAM, UC3M, UCM, UPM y URJC
- Sesion doble –

Asymptotic behaviour for nonlocal diffusion-convection equations 1

Prof. Liviu Ignat
Institute of Mathematics Simion Stoilow

On the boundedness of spherical maximal function on Heisenberg 2
groups

Prof. Sundaram Thangavelu
Indian Institute of Sciences of Bangalore

Jueves 25 de octubre de 2018, 12:00 y 12:45
Seminario del Departamento de Matemáticas, aula C-17-520
U. Autónoma de Madrid

Resumen1. In this talk we analyze the long time behaviour of the solutions of the equation
ut (t,x) + L u(t,x) + (f(u))x = 0, t>0, x ∈ R,
where L is a nonlocal operator and f(s)=|s|^{q-1}s/q with q>1. When L = (-Δ)α/2 we prove that
in the one-dimensional case, for 1<q<α<2 the asymptotic behaviour is given by the entropy
solution of the conservation law ut(t,x)+(f(u))x = 0, u(0)=Mδ0 where M is the mass of the initial
data. The proof relays on tricky inequalities to guarantee an Oleinik type inequality. Joint work
with Diana Stan.

Resumen2. In this talk we plan to report some ongoing joint work with Bagchi, Hait and Roncal
on the Lp boundedness of the lacunary maximal function associated to the spherical means on
the Heisenberg group.
Organizado por los proyectos: MTM2017-85757-P, MTM2017-87596-P
Comité organizador: Matteo Bonforte, Mar González, Arturo de Pablo y Fernando Quirós