Asymptotics for evolution problems with nonlocal diffusion
Julio Daniel Rossi,
IMDEA Prof. (IMDEA Matematicas, Madrid, Espaņa)
Associate Prof. (University of Buenos Aires, Argentina) (on leave).
Independent Researcher (CONICET, Argentina) (on leave).
Jueves 24 de abril 2008
In this talk we will review recent results concerning
solutions to nonlocal evolution equations with different boundary
conditions, Dirichlet or Neumann and even for the Cauchy problem.
We deal with existence/uniqueness of solutions and their
asymptotic behavior. We also review some recent results concerning
limits of solutions to nonlocal equations when a rescaling
parameter goes to zero. We recover in these limits some of the
most frequently used diffusion models: the heat equation with
Neumann or Dirichlet boundary conditions, the $p-$Laplace
evolution equation with Neumann boundary conditions and a
convection-diffusion equation.