A model of tumor growth in a spatial environment is analyzed. The model includes
proliferating and quiescent compartments of tumor cells indexed by successively mutated cell phenotypes
of increasingly proliferative aggressiveness. The model incorporates spatial dependence
due to both random motility and directed movement haptotaxis. The model structures tumor cells
by both cell age and cell size. The model consists of a system of nonlinear partial differential
equations for the compartments of tumor cells, extracellular matrix, matrix degradative enzyme,
and oxygen. The existence, uniqueness, positivity, regularity, and growth characteristics of the
solutions are investigated.