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Global solution and global orbit to reaction–diffusion equation for fractional Dirichlet‐to‐Neumann operator with subcritical exponent
Author(s) -
Tan Zhong,
Xie Minghong
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6888
Subject(s) - mathematics , exponent , mathematical analysis , operator (biology) , dirichlet distribution , orbit (dynamics) , diffusion equation , reaction–diffusion system , boundary value problem , economy , service (business) , philosophy , linguistics , biochemistry , chemistry , repressor , transcription factor , engineering , gene , aerospace engineering , economics
We consider the reaction–diffusion equation for fractional Dirichlet‐to‐Neumann operator with subcritical exponent motivated by electrical impedance tomography (EIT) and a need to overcome the non‐locality of a fractional differential equation for modeling anomalous diffusion. We mainly deal with the asymptotic behavior of global solution and the boundedness of global orbit, which allows us to show that any global solution is classical solution using Moser iteration technique.