The well‐posedness and long‐time behavior of the nonlocal diffusion porous medium equations with nonlinear term

摘要

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. First, we obtain the well‐posedness of the solutions in L1(Ω) for the equations. Second, 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.