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Aggregation equations with gradient potential as Radon measure and initial data in Besov‐Morrey spaces
Author(s) -
Suleiman Marta L.,
Precioso Juliana C.,
Prokopczyk Andréa C.
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.6355
Subject(s) - radon measure , mathematics , measure (data warehouse) , nonlinear system , mathematical analysis , work (physics) , class (philosophy) , stability (learning theory) , exponential stability , similarity (geometry) , pure mathematics , physics , thermodynamics , computer science , database , artificial intelligence , machine learning , image (mathematics) , locally compact space , quantum mechanics
In this work, we present conditions to obtain a global‐in‐time existence of solutions to a class of nonlinear viscous transport equations describing aggregation phenomena in biology with sufficiently small initial data in Besov‐Morrey spaces and gradient potential as a Radon measure. We also study the self‐similarity and asymptotic stability of solutions at large times.