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The well-posedness and long-time behavior of the nonlocal diffusion porous medium equations with nonlinear term
  • Chang Zhang,
  • Fengjuan Meng,
  • Cuncai Liu
Chang Zhang
Jiangsu University of Technology

Corresponding Author:[email protected]

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Fengjuan Meng
Jiangsu University of Technology
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Cuncai Liu
Jiangsu University of Technology
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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.
19 Oct 2021Submitted to Mathematical Methods in the Applied Sciences
20 Oct 2021Submission Checks Completed
20 Oct 2021Assigned to Editor
26 Oct 2021Reviewer(s) Assigned
23 Nov 2021Review(s) Completed, Editorial Evaluation Pending
23 Nov 2021Editorial Decision: Revise Minor
23 Nov 20211st Revision Received
24 Nov 2021Submission Checks Completed
24 Nov 2021Assigned to Editor
26 Nov 2021Reviewer(s) Assigned
27 Nov 2021Review(s) Completed, Editorial Evaluation Pending
27 Nov 2021Editorial Decision: Accept
22 Dec 2021Published in Mathematical Methods in the Applied Sciences. 10.1002/mma.8055