2 research outputs found
Nonlocal and nonlinear evolution equations in perforated domains
In this work we analyze the behavior of the solutions to nonlocal evolution
equations of the form with in a perturbed domain which is thought as a fixed set from where we remove a subset
called the holes. We choose an appropriated families of functions
in order to deal with both Neumann and Dirichlet
conditions in the holes setting a Dirichlet condition outside .
Moreover, we take as a non-singular kernel and as a nonlocal
nonlinearity. % Under the assumption that the characteristic functions of
have a weak limit, we study the limit of the solutions
providing a nonlocal homogenized equation