ABSTRACT

This chapter considers the decay of solutions to the Korteweg de Vries-Burger equation, to scalar parabolic conservation laws in several space dimensions, and to parabolic systems of conservation laws in one space dimension. For the Korteweg de Vries-Burger equation, it obtains decay at a uniform algebraic rate for the solution of the Cauchy problem. For the scalar parabolic conservation law, the chapter establishes uniform rates of decay for the solution of the Cauchy problem.