Universidad de Alicante y Buenos Aires

In these notes we 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.