  A continuum grain boundary model is developed that uses experimentally
measured grain boundary energy data as a function of misorientation to simulate
idealized grain boundary evolution in a 1-D grain array. The model uses a
continuum representation of the misorientation in terms of spatial gradients of
the orientation as a fundamental field. The grain boundary energy density
employed is non-convex in this orientation gradient, based on physical grounds.
Simple gradient descent dynamics of the energy are utilized for idealized
microstructure evolution, which requires higher-order regularization of the
energy density for the model to be well-set; the regularization is physically
justified. Microstructure evolution is presented using two plausible energy
density functions, both defined from the same experimental data: a 'smooth' and
a 'cusp' energy density. Results of grain boundary equilibria and
microstructure evolution representing grain reorientation in one space
dimension are presented. The different shapes of the energy density functions
representing a common data set are shown to result in different overall
microstructural evolution of the system. Mathematically, the constructed energy
functional formally is of the Aviles-Giga/Cross-Newell type but with unequal
well-depths, resulting in a difference in the structural feature of solutions
that can be identified with grain boundaries, as well as in the approach to
equilibria from identical initial conditions. This study also investigates the
metastability of grain boundaries. It supports the general thermodynamics
belief that they persist for extended periods before eventually vanishing due
to the lowest energy configuration favored by fluctuations over infinite time.
