Symmetry and Integrability of Equations of Mathematical Physics − 2013

Maksym Didovych (Institute of Mathematics of NAS of Ukraine, Kyiv, Ukraine)

The simplified Keller-Segel model: Lie symmetries, plane wave exact solutions, linearization and Cauchy problem

Lie symmetries of a simplified Keller-Segel system are found and applied for construction of exact solutions. Several families of such solutions in an explicit form are found, their properties examined and possible applicability for chemotaxis modeling is discussed. Linearization of the system and its Cauchy problem solution are presented.