Qualitative analysis and simulations of a free boundary problem for multispecies biofilm models
The work presents an analysis of solutions to a free boundary value problem for a multispecies biofilm growth model in one space dimension. The mathematical model consists of a system of nonlinear partial differential equations and a free boundary. It is quite general and can include a large variety of special situations. An existence and uniqueness theorem is discussed and properties of solutions are given. As a numerical application, simulations for a heterotrophic-autotrophic competition are developed by the method of characteristics. (C) 2010 Elsevier Ltd. All rights reserved.
free boundary problems biofilm mathematical modelling method of characteristics nonlinear hyperbolic and parabolic partial differential equations