  Chronic wounds represent a major public health problem affecting 6.5 million
people in the United States. Ischemia represents a serious complicating factor
in wound healing. In this paper we analyze a recently developed mathematical
model of ischemic dermal wounds. The model consists of a coupled system of
partial differential equations in the partially healed region, with the wound
boundary as a free boundary. The extracellular matrix (ECM) is assumed to be
viscoelastic, and the free boundary moves with the velocity of the ECM at the
boundary of the open wound. The model equations involve the concentrations of
oxygen, cytokines, and the densities of several types of cells. The ischemic
level is represented by a parameter which appears in the boundary conditions, 0
<= gamma < 1; gamma near 1 corresponds to extreme ischemia and gamma = 0
corresponds to normal non-ischemic conditions. We establish global existence
and uniqueness of the free boundary problem and study the dependence of the
free boundary on gamma.
