A Constructive Approach to Traveling Waves in Chemotaxis
نویسندگان
چکیده
In this paper we study the existence of one and multidimensional traveling wave solutions for general chemotaxis or so-called Keller-Segel models without reproduction of the chemotactic species. We present a constructive approach to give modelers a choice of chemotactic sensitivity functionals, production, and degradation terms for the chemical signal at hand. The main aim is to understand the type of functionals and the interplay between them which are needed for the traveling wave and pulse patterns to occur.
منابع مشابه
Nonlinear Stability of Large Amplitude Viscous Shock Waves of a Generalized Hyperbolic{parabolic System Arising in Chemotaxis
Traveling wave (band) behavior driven by chemotaxis was observed experimentally by Adler and was modeled by Keller and Segel. For a quasilinear hyperbolic parabolic system that arises as a non-di®usive limit of the Keller Segel model with nonlinear kinetics, we establish the existence and nonlinear stability of traveling wave solutions with large amplitudes. The numerical simulations are perfor...
متن کاملMathematics of Traveling Waves in Chemotaxis –review Paper–
This article surveys the mathematical aspects of traveling waves of a class of chemotaxis models with logarithmic sensitivity, which describe a variety of biological or medical phenomena including bacterial chemotactic motion, initiation of angiogenesis and reinforced random walks. The survey is focused on the existence, wave speed, asymptotic decay rates, stability and chemical diffusion limit...
متن کاملTraveling Pulses for a Two-Species Chemotaxis Model
Mathematical models have been widely used to describe the collective movement of bacteria by chemotaxis. In particular, bacterial concentration waves traveling in a narrow channel have been experimentally observed and can be precisely described thanks to a mathematical model at the macroscopic scale. Such model was derived in [1] using a kinetic model based on an accurate description of the mes...
متن کاملTraveling Waves of Some Symmetric Planar Flows of Non-Newtonian Fluids
We present some variants of Burgers-type equations for incompressible and isothermal planar flow of viscous non-Newtonian fluids based on the Cross, the Carreau and the power-law rheology models, and on a symmetry assumption on the flow. We numerically solve the associated traveling wave equations by using industrial data and in order to validate the models we prove existence and uniqueness of ...
متن کاملPerron Theorem in the Monotone Iteration Method for Traveling Waves in Delayed Reaction-diffusion Equations
In this paper we revisit the existence of traveling waves for delayed reaction diffusion equations by the monotone iteration method. We show that Perron Theorem on existence of bounded solution provides a rigorous and constructive framework to find traveling wave solutions of reaction diffusion systems with time delay. The method is tried out on two classical examples with delay: the predator-p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Nonlinear Science
دوره 14 شماره
صفحات -
تاریخ انتشار 2004