Absence of collapse in a parabolic chemotaxis system with signal‐dependent sensitivity | Zendy

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Absence of collapse in a parabolic chemotaxis system with signal‐dependent sensitivity

Author(s) -

Winkler Michael

Publication year - 2010

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.200810838

Subject(s) - chemotaxis , bounded function , neumann boundary condition , mathematics , domain (mathematical analysis) , mathematical analysis , homogeneous , sensitivity (control systems) , boundary value problem , boundary (topology) , function (biology) , combinatorics , chemistry , receptor , biochemistry , electronic engineering , evolutionary biology , engineering , biology

We consider the chemotaxis systemunder homogeneous Neumann boundary conditions in a smooth bounded domain Ω ⊂ ℝ n . The chemotactic sensitivity function is assumed to generalize the prototypeIt is proved that no chemotactic collapse occurs in the sense that for any choice of nonnegative initial data (with some r > n ), the corresponding initial‐boundary value problem possesses a unique global solution that is uniformly bounded (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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