The well-posedness and long-time behavior of the nonlocal diffusion
porous medium equations with nonlinear term
Abstract
In this paper, we mainly consider the well-posedness and long-time
behavior of solutions for the nonlocal diffusion porous medium equations
with nonlinear term. Firstly, we obtain the well-posedness of the
solutions in L1(Ω) for the equations. Secondly, we prove the existence
of a global attractor by proving there exists a compact absorbing set.
Finally, we apply index theory to consider the dimension of the
attractor and prove that there exists an infinite dimensional attractor
of the equations under proper conditions.