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From 1970 until present: the Keller-Segel model in chemotaxis and its consequences. II. (English) Zbl 1072.35007
Summary: This second part of the survey on the Keller-Segel model continues to summarize various aspects and results for some general formulations of the classical chemotaxis model started in [ibid. 105, No. 3, 103–165 (2003; Zbl 1071.35001)]. This part will concentrate on existence results of self-similar solutions and on traveling wave solutions for the Keller-Segel model in chemotaxis.

MSC:
35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35J20 Variational methods for second-order elliptic equations
35J25 Boundary value problems for second-order elliptic equations
35J65 Nonlinear boundary value problems for linear elliptic equations
35K50 Systems of parabolic equations, boundary value problems (MSC2000)
35K57 Reaction-diffusion equations
92C17 Cell movement (chemotaxis, etc.)
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