| Summary: In this study, an existing wound-slough interaction model has been analysed in detail and to account for the effects of physiological dimension it is extended to a model which turned out to be a nonlinear system of partial differential equations, refer to as WSPDE. Having obtained dimensionless WSPDE model first corresponding stationary model has been analysed by means of lower and upper solutions of stationary system. Existence, uniqueness and nonnegativity of solutions with Dirichlet boundary conditions was proven. Furthermore the model has been extended 2-dimensional and 3-dimensional systems and the resulting extended models have been solved numerically using effective algorithms to investigate wound-slough interaction. With physiological parameters it was observed no diffusive instability can arise. Next, in case when slough-wound interaction leads to unhealing wounds debridement strategy, as usually performed by surgeons, has been incorpareted into the model and effect of debridement on wound healing has been observed in models. Finally upper and lower solutions for travelling waves have been shown and travelling wave solutions have been observed numerically.
Key Words: Mathematical Model of Wound-Slough Interaction, Travelling Wave Solutions, Upper and Lower Solutions |
