The effect of non-local convection on reaction-diffusion equations
The equation (1) \(\partial u/\partial t=\partial /\partial x\{\partial u/\partial x-(K*u)u\}+\epsilon f(u)\) is investigated. K*u denotes the convolution with kernel \(K(x)=-r\) \((x>0)\) or \(+r\) \((x<0)\), where r is a positive constant. The author shows that if \(\epsilon >0\) is sufficiently small, the study of the existence and their stability of stationary solutions of (1) are reduced to investigate zeros and the sign of a derivative at each zero of some function F. He also investigates the effect of such a non-local convection on the behavior of solutions by using the function F.
scientific article; zbMATH DE number 4036299