Global Existence of solutions to Reaction-Diffusion Systems with Mass Transport type Boundary Conditions

We consider coupled reaction-diffusion models, where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. We proved if vector fields are locally Lipschitz functions and satisfies quasi-positivity conditions, and if initial data are component-wise bounded and non-negative then there exists T_max >0 such that our model has component-wise non-negative solution with T = T_max. Our criterion for determining local existence of the solution involves derivation of a priori estimates, as well as regularity of the solution, and the use of a fixed point theorem. Moreover, if vector fields satisfies certain conditions explained in dissertation, then there exists solution for all time, t>0. Classical potential theory and estimates for linear initial boundary value problems are used to prove local well-posedness and global existence. This type of system arises in mathematical models for cell processes.