Abstract
The mathematical model for subdiffusion process with chemotaxis proposed by Langlands and Henry [1] for the one-dimensional case is extended to the multi-dimensional case. The model is derived from random walks process using a probability measure on a n-multidimensional unit ball $S^{n-1}$.
Highlights
Consider the chemotaxis-diffusion system ( )where is a bounded domain with boundary
We consider a particle moving in a random walk process
We suppose ( ), ( ), and ( ) stand for the jump probability of the particle in the direction from position at time, the waiting time probability of the particle to jump after waiting a time
Summary
Consider the chemotaxis-diffusion system ( )where is a bounded domain with boundary. The System Eq (1)-(4)is well known as the Keller-Segel Chemotaxis (KS) model. The model (KS) describes the space and time evolution of the concentration of diffusing amoebae that is chemotactically attracted by diffusing acrasin (see [2]). Langlands and Henry [1] derived an equation describing the process in which the attracted species moves subdiffusively, which is called by the fractional chemotaxis-diffusion equation for the one-dimensional case.
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