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Blow‐up phenomena in chemotaxis systems with a source term
Author(s) -
Marras Monica,
VernierPiro Stella,
Viglialoro Giuseppe
Publication year - 2016
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.3728
Subject(s) - mathematics , term (time) , bounded function , domain (mathematical analysis) , boundary (topology) , type (biology) , mathematical analysis , chemotaxis , parabolic partial differential equation , boundary value problem , partial differential equation , physics , receptor , quantum mechanics , biology , ecology , biochemistry , chemistry
This paper deals with a parabolic–parabolic Keller–Segel‐type system in a bounded domain ofR N , { N = 2;3}, under different boundary conditions, with time‐dependent coefficients and a positive source term. The solutions may blow up in finite time t ∗ ; and under appropriate assumptions on data, explicit lower bounds for blow‐up time are obtained when blow up occurs. Copyright © 2015 John Wiley & Sons, Ltd.