BIFURCATION OF SOLUTIONS TO THE CONTROLLED BURGERS-EQUATION

Abstract

In this paper we study the stability and the bifurcation of the equilibrium solution of a controlled Burgers equation

an integral term. representing a non-local behavior, has been added to the normal form of the equation describing flow through porous media. We find that a supercritical bifurcation from the rest solution occurs if the viscosity is reduced below a critical value. This value is calculated as a function of the porosity coefficient and the corresponding bifurcation solution is derived using- perturbation forms up to fourth order.