Related papers: Boundedness in a nonlinear chemotaxis-consumption …
Cells sense environmental signals and transmit information intracellularly through changes in the abundance of molecular components. Such molecular abundances can be measured in single cells and exhibit significant heterogeneity in clonal…
We consider various modeling levels for spatially homogeneous chemical reaction systems, namely the chemical master equation, the chemical Langevin dynamics, and the reaction-rate equation. Throughout we restrict our study to the case where…
We study the diffusion of a tracer particle driven out-of-equilibrium by an external force and traveling in a dense environment of arbitrary density. The system evolves on a discrete lattice and its stochastic dynamics is described by a…
We consider the chemotaxis problem for a one-dimensional system. To analyze the interaction of bacteria and attractant we use a modified Keller-Segel model which accounts attractant absorption. To describe the system we use the chemotaxis…
We consider the well-posedness of models involving age structure and non-linear diffusion. Such problems arise in the study of population dynamics. It is shown how diffusion and age boundary conditions can be treated that depend…
A novel principle is presented which allows for the proof of bounded weak solutions to a class of physically relevant, strongly coupled parabolic systems exhibiting a formal gradient-flow structure. The main feature of these systems is that…
The current series of research papers is to investigate the asymptotic dynamics in logistic type chemotaxis models in one space dimension with a free boundary or an unbounded boundary. Such a model with a free boundary describes the…
The nonlinear diffusion in multicomponent liquids under chemical reactions influence has been studied. The theory is applied to the analysis of mass transfer in a solution of acetone-benzene. It has been shown, that the creation of…
We consider processes that coincide with a given diffusion process except on the boundaries of a finite collection of domains. The behavior on each of the boundaries is asymmetric: the process is much more likely to enter the interior of…
Chemotaxis plays a crucial role in a variety of processes in biology and ecology. Quite often it acts to improve efficiency of biological reactions; one example is the immune system signalling, where infected tissues release chemokines…
We consider nonlinear elliptic systems satisfying componentwise coercivity condition. The nonlinear terms have controlled growths with respect to the solution and its gradient, while the behaviour in the independent variable is governed by…
This paper deals with a nonlinear system of partial differential equations modeling a simplified tumor-induced angiogenesis taking into account only the interplay between tumor angiogenic factors and endothelial cells. Considered model…
Cells are constantly exposed to diverse stimuli-chemical, mechanical, or electrical-that guide their movement. In physiological conditions, these signals often overlap, as seen during infections, where neutrophils and dendritic cells…
The problem of load balancing in a distribution network under unknown time- varying demand and supply is studied. A set of distributed controllers which regulate the amount of flow through the edges is designed to guarantee convergence of…
We give a comprehensive study of the analytic properties and long-time behavior of solutions of a reaction-diffusion system in a bounded domain in the case where the nonlinearity satisfies the standard monotonicity assumption. We pay the…
Cells respond to chemical cues, and the precision with which they can sense these cues is fundamentally limited by the stochastic nature of diffusion and ligand binding. Berg and Purcell famously investigated how well a small sensor in an…
In this paper the first equation within a class of well known chemotaxis systems is derived as a hydrodynamic limit from a stochastic interacting many particle system on the lattice. The cells are assumed to interact with attractive…
Phase separation in passive systems leads to uncontrolled droplet growth, limiting structural control in soft materials and cells. We identify a generic mechanism to arrest coarsening based on chemical interconversion between molecular…
The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying…
The current series of research papers is to investigate the asymptotic dynamics in logistic type chemotaxis models in one space dimension with a free boundary or unbounded boundary. Such a model with a free boundary describes the spreading…