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.