Largest well-posed spaces for the general diffusion system with nonlocal interactions

摘要

The authors derive a general diffusion (GD) system with non local interactions of special structure via energetic variational approach and observe that there exist two critical values of s, i.e. s = 1/2, 1, for the nonlocal interactions, where s = 1/2 reflects how strong nonlocal property we have and s = 1 affects the linearization and choice of initial data spaces. The authors also establish the global existence and uniqueness of mild solution. (C) 2017 Elsevier Inc. All rights reserved.