SOLVING A NONLINEAR PSEUDO-DIFFERENTIAL EQUATION OF BURGERS TYPE.

In this paper, we study the initial value problem for a class of nonlinear equations of Burgers type in the following form: \[ \frac{\partial}{\partial t}u + \nu q(x,D)u + (b \cdot \nabla)f(u) = 0 \] for u:(t,x) ∈ (0,∞) × ℝn ↦ ℝ, where q(x,D) is a pseudo-differential operator with negative definite symbol. We solve the initial value problem for the equation on ℝn by utilising a fix point argument based upon a combination of semigroup approach and Hoh's symbolic calculus. [ABSTRACT FROM AUTHOR]