Seyrich, Maximilian

Das Darmbakterium Escherichia coli (E.coli ) ist in den Bereichen der Molekularbiologie, der Zellbiologie und des Forschungsfeldes der Mikroschwimmer eines der am besten erforschten Lebewesen. Die vorliegende Arbeit leistet einen Beitrag zur Grundlagenforschung der Chemotaxis von E.coli (gerichtete Bewegung entlang eines externen chemischen Stimulu...

Davis, Paige van Heijster, Petrus Marangell, Robert

We investigate the point spectrum associated with travelling wave solutions in a Keller–Segel model for bacterial chemotaxis with small diffusivity of the chemoattractant, a logarithmic chemosensitivity function and a constant, sublinear or linear consumption rate. We show that, for constant or sublinear consumption, there is an eigenvalue at the o...

Jabir, Jean-Francois Talay, Denis Tomasevic, Milica

In this work, we prove the well–posedness of a singularly interacting stochastic particle system and we establish propagation of chaos result towards the one-dimensional parabolic-parabolic Keller-Segel model.

Giani Egana, Fernandez Mischler, Stéphane

The present paper deals with the parabolic-elliptic Keller-Segel equation in the plane in the general framework of weak (or ''free energy") solutions associated to initial datum with finite mass $M$, finite second moment and finite entropy. The aim of the paper is threefold: (1) We prove the uniqueness of the ''free energy" solution on the maximal ...

Cattiaux, Patrick Pédèches, Laure

We introduce a stochastic system of interacting particles which is expected to furnish as the number of particles goes to infinity a stochastic approach of the 2-D Keller-Segel model. In this note, we prove existence and some uniqueness for the stochastic model for the parabolic-elliptic Keller-Segel equation, for all regimes under the critical mas...

Blanchet, Adrien Carrillo, José Kinderlehrer, David Kowalczyk, Michal Laurençot, Philippe Lisini, Stefano

We construct weak global in time solutions to the classical Keller-Segel system cell movement by chemotaxis in two dimensions when the total mass is below the well-known critical value. Our construction takes advantage of the fact that the Keller-Segel system can be realized as a gradient flow in a suitable functional product space. This allows us ...

Montaru, Alexandre

This thesis is concerned with the study of two problems : On the one hand, we consider a parabolic-elliptic system of Patlak-Keller-Segeltype with a critical power type sensitivity. We study the radially symmetric solutions of this system on a ball of the euclidean space and obtain wellposedness and regularity results together with a blow-up altern...

Nasreddine, Elissar
Published in
Journal of Mathematical Analysis and Applications

This paper is devoted to the analysis of nonnegative solutions for a degenerate parabolic–elliptic Patlak–Keller–Segel system with critical nonlinear diffusion in a bounded domain with homogeneous Neumann boundary conditions. Our aim is to prove the existence of a global weak solution under a smallness condition on the mass of the initial data, the...

Campos Serrano, Juan Dolbeault, Jean

We investigate the large-time behavior of the solutions of the two-dimensional Keller-Segel system in self-similar variables, when the total mass is subcritical, that is less than 8π after a proper adimensionalization. It was known from previous works that all solutions converge to stationary solutions, with exponential rate when the mass is small....

Ramakrishnan, S Laurent, T Kumar, M Bertozzi, AL

© 2014 World Scientific Publishing Company. In this paper, we present a generic theoretical chemotactic model that accounts for certain emergent behaviors observed in ant foraging. The model does not have many of the constraints and limitations of existing models for ants colony dynamics and takes into account the distinctly different behaviors exh...