The incompatibilities between the initial and boundary data will cause
singularities at the time-space corners, which in turn adversely affect the
accuracy of the numerical schemes used to compute the solutions. We study the
corner singularity issue for nonlinear evolution equations in 1D, and propose
two remedy procedures that effectively recover much of the accuracy of the
numerical scheme in use. Applications of the remedy procedures to the 1D
viscous Burgers equation, and to the 1D nonlinear reaction-diffusion equation
are presented.