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 …

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 …

Critical mass for infinite-time aggregation in a chemotaxis model with indirect signal production
Page 1 DOI 10.4171/JEMS/749 J. Eur. Math. Soc. 19, 3641–3678 c European Mathematical …

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 …

The 8-problem for radially symmetric solutions of a chemotaxis model in the plane Page 1
MATHEMATICAL METHODS IN THE APPLIED SCIENCES Math. Meth. Appl. Sci. 2006; 29:1563–1583 …

We study the blow-up asymptotics of radially decreasing solutions of the parabolic–elliptic
Keller–Segel–Patlak system in space dimensions n ≧ 3 n≥ 3. In view of the biological …

PIOTR BILER(WROC LAW) This is the third part of the study [7, 9]. We consider here local-in-
t ime solutions of the parabolic-elliptic system from [9,(1)–(5)], which cannot be extended for …

We propose and analyze a novel approach to construct structure preserving approximations
for the Poisson–Nernst–Planck equations, focusing on the positivity preserving and mass …

We discuss the existence of the blow-up solution for some nonlinear parabolic system called
attractive drift-diffusion equation in two space dimensions. We show that if the initial data …