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The role of a strong confining potential in a nonlinear Fokker-Planck equation

Abstract:

We show that solutions of nonlinear nonlocal Fokker--Planck equations in a bounded domain with no-flux boundary conditions can be approximated by Cauchy problems with increasingly strong confining potentials defined in the whole space. Two different approaches are analyzed, making crucial use of uniform estimates for $L^2$ energy functionals and free energy (or entropy) functionals respectively. In both cases, we prove that the weak formulation of the problem in a bounded domain can be obtain...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1016/j.na.2019.03.003

Authors


Publisher:
Elsevier Publisher's website
Journal:
Nonlinear Analysis: Theory, Methods and Applications Journal website
Volume:
193
Issue:
2020
Article number:
111480
Publication date:
2019-03-28
Acceptance date:
2019-03-02
DOI:
EISSN:
1873-5215
ISSN:
0362-546X
Language:
English
Keywords:
Pubs id:
1098214
Local pid:
pubs:1098214
Deposit date:
2020-04-02

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