A (1+2)-dimensional simplified Keller-Segel model: Lie symmetry and exact solutions (Q2406232)

Summary: This research is a natural continuation of the recent paper [\textit{R. Cherniha} and the author, Commun. Nonlinear Sci. Numer. Simul. 18, No. 11, 2960--2971 (2013; Zbl 1329.35167)]. It is shown that a (1+2)-dimensional Keller-Segel type system is invariant with respect infinite-dimensional Lie algebra. All possible maximal algebras of invariance of the Neumann boundary value problems based on the Keller-Segel system in question were found. Lie symmetry operators are used for constructing exact solutions of some boundary value problems. Moreover, it is proved that the boundary value problem for the (1+1)-dimensional Keller-Segel system with specific boundary conditions can be linearized and solved in an explicit form.