The generalized Burgers equation with and without a time delay (Q1773280)

The paper deals with the following generalized Burgers equation with time delay and periodic boundary condition \[ \begin{alignedat}{2} u_t(x,t) &= \nu u_{xx}(x,t) - u(x,t-\tau)u_x(x,t) + u(x,t), &\quad 0 &< x < 2\pi, \;t >0,\\ u(0,t) &= u(2\pi,t), &\quad t&>0,\\ u(x,s) &= u_0(x,s), &\quad 0&<x<2\pi, \;-\tau \leq s \leq 0. \end{alignedat} \] The authors show that the equation under consideration is exponentially stable under small delays. Using a pseudospectral method adequate numerical results are presented.