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.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Houston

Year dc:date.issued

2013

Author dc:creator

• Sharma, Vandana 1984-

Advisor dc:contributor.advisor

• Morgan, Jeff

Committee members dc:contributor.committeemember

• Fitzgibbon, William E.
• Canic, Suncica
• Pavlidis, Ioannis T.

• Global Existence
• Manifold
• Conservation of mass
• Mass Transport
• Reaction-Diffusion Systems
• Laplace Beltrami Operator

Statement dc:rights

• The 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).

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/10657/1040

OAI identifier oai:identifier

oai:uh-ir.tdl.org:10657/1040