Morgan, Jeff2015-08-242015-08-24August 2012013-08http://hdl.handle.net/10657/1040We 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.application/pdfengThe author of this work is the copyright owner. UH Libraries and the Texas Digital Library have their permission to store and provide access to this work. Further transmission, reproduction, or presentation of this work is prohibited except with permission of the author(s).Global ExistenceManifoldConservation of massMass TransportReaction-Diffusion SystemsLaplace Beltrami OperatorMathematics2015-08-24Thesisborn digital