کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1898558 1044734 2012 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On spectra of linearized operators for Keller–Segel models of chemotaxis
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
On spectra of linearized operators for Keller–Segel models of chemotaxis
چکیده انگلیسی

We consider the phenomenon of collapse in the critical Keller–Segel equation (KS) which models chemotactic aggregation of micro-organisms underlying many social activities, e.g. fruiting body development and biofilm formation. Also KS describes the collapse of a gas of self-gravitating Brownian particles. We find the fluctuation spectrum around the collapsing family of steady states for these equations, which is instrumental in the derivation of the critical collapse law. To this end we develop a rigorous version of the method of matched asymptotics for the spectral analysis of a class of second order differential operators containing the linearized Keller–Segel operators (and as we argue linearized operators appearing in nonlinear evolution problems). We explain how the results we obtain are used to derive the critical collapse law, as well as for proving its stability.


► Critical Keller–Segel equation models chemotactic aggregation of micro-organisms.
► Found the fluctuation spectrum around the collapsing family of steady states.
► Develop a rigorous version of the method of matched asymptotics.
► Found low-lying eigenvalues for linearization about approximate collapsing solutions.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physica D: Nonlinear Phenomena - Volume 241, Issue 15, 1 August 2012, Pages 1245–1254
نویسندگان
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