On Moving Boundaries in Elliptic—Parabolic Systems
Joachim Escher · Birkhäuser Basel eBooks · 2003
Of concern is a simple model describing in vivo cancer growth for a single tumor. The model comprises a reaction-diffusion equation describing the evolution of the nutrient concentration, denoted by u and an elliptic equation for the internal pressure, denoted by p , in the tissue. The cell proliferation rate is denoted by f(u) , where f : ℝ → ℝ is assumed to be smooth. At time t the tumor occupies the domain Ω( t ) with the moving boundary Г( t ). In dimensionless form p and u satisfy the equations These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.