On the evolution of solutions of Burgers equation on the positive quarter-plane

Abstract

In this paper we investigate an initial-boundary value problem for the Burgers equation on the positive quarter-plane;

v(t) + vv(x) - v(xx) = 0, x > 0, t > 0,

v(x, 0) = u+, x > 0,

v(0, t) = u(b), t > 0,

where x and t represent distance and time, respectively, and u(+) is an initial condition, u(b) is a boundary condition which are constants (u(+) not equal u(b)). Analytic solution of above problem is solved depending on parameters (u(+) and u(b)) then compared with numerical solutions to show there is a good agreement with each solutions.