In 1970 Keller and Segel [15] proposed a mathematical model describing chemotactic
aggregation of cellular slime molds which move preferentially towards relatively high …

We consider theinitial-boundary value problem ofparabolic-elliptic systems on bounded
domains in 2 with smoothboundary which is a mathematical model of chemotaxis. Making a …

Γ vt= v− λv+ u in Ω×(0, T), in a domain Ω of RN with N⩾ 1, where m, Γ> 0, λ⩾ 0 are constants
and T> 0. When Ω= RN, we impose the Neumann boundary conditions on the boundary …

Existence of local and global in time solutions for parabolic-elliptic and parabolic systems
describing the aggregation of the cellular slime mould by the chemical attraction is studied …

We obtain a priori estimates for the classical chemotaxis model of Patlak, Keller and Segel
when a nonlinear diffusion or a nonlinear chemosensitivity is considered accounting for the …

This chapter returns to the general W (x) and describes the fact that the varia-tional structure
F defined on Pλ and that of Jλ on V= dom (A 1/2) stated in Chapter 6 are equivalent up to …

PDE systems describing chemotaxis, the directed motion of organisms in response to a
chemical signal, contain a cross-diffusive term which in many cases causes the …

appeared in Adv. Math. Sci. Appl. 9 (1999), 347–359. GLOBAL SOLUTIONS TO SOME
PARABOLIC-ELLIPTIC SYSTEMS OF CHEMOTAXIS Piotr B Page 1 appeared in Adv. Math …

We consider the degenerate Keller-Segel system (KS) of Nagai type below. We prove that
when m>2-2N, the problem (KS) is solvable globally in time without any restriction on the …

We study a system consisting of the elliptic-parabolic Keller–Segel equations coupled to
Stokes equations by transport and gravitational forcing. We show global-in-time existence of …