Solutions to problems from part 7

Abstract

J. Zhang [1] has studied the system (2.19)—(2.22) which is a conservation law, with nonlocal terms, in the bounded region

$$\left\{ {{x_1} > 0,{x_2} > 0, \ldots ,{x_m} > 0,{x_1} + {x_2} + \cdots + {x_m} = 1} \right\}$$

(4.1)

. He proved existence and uniqueness of the solution, and obtained numerical results for the intermediate and long term behavior of the solution when the initial data consists of several “hills.”