Abstract
Diffusion-Reaction (DR) equation has been used to model a large number of phenomena in nature. It may be mentioned that a linear diffusion equation does not exhibit any traveling wave solution. But there are a vast number of phenomena in different branches not only of science but also of social sciences where diffusion plays an important role and the underlying dynamical system exhibits traveling wave features. In contrast to the simple diffusion when the reaction kinetics is combined with diffusion, traveling waves of chemical concentration are found to exist. This can affect a biochemical change, very much faster than straight diffusional processes. This kind of coupling results into a nonlinear (NL) DR equation. In recent years, memory effect in DR equation has been found to play an important role in many branches of science. The effect of memory enters into the dynamics of NL DR equation through its influence on the speed of the travelling wavefront. In the present work, chemotaxis equation with source term is studied in the presence of finite memory and its solution is compared with the corresponding chemotaxis equation without finite memory. Also, a comparison is made between Fisher-Burger equation and chemotaxis equation in the presence of finite memory. We have shown that nonlinear diffusion-reaction-convection equation is equivalent to chemotaxis equation.
Highlights
Diffusion-Reaction (DR) equation has been used to explain many phenomena in nature [1]
Convective velocity is a measure of the bias in the system
Certain aspects ignored earlier [10] in the studies of the chemotaxis equation involving quadratic nonlinearity are investigated in this work
Summary
Diffusion-Reaction (DR) equation has been used to explain many phenomena in nature [1]. There are many phenomena in nature in which convection velocity term becomes important [11]-[13]. Nonlinear convective flux term arises naturally in the study of chemotaxis equation [15]. Insects, single cell organism, bacteria and animals rely on an acute sense of smell for conveying information between members of the species and the chemicals which are involved in this process are called pheromones. The acute sense of smell of many deep sea fish is important for communication and predation [1] [20] It is in animal and insect ecology that the mechanism of chemotaxis is important. We will discuss memory effect in DR equation
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