Author

Sahitya Konda

Publication Date

9-1-2015

Abstract

In this thesis, we consider the system of reaction-diffusion equations and the behavior of the solution of such a system. The focus is to concentrate on solutions which decay at infinity. Under suitable assumptions, we prove the solution and its derivatives decay exponentially in all space. We also attempt to show that the solution decays exponentially for the system of equations when posed on a finite disk. This result has been confirmed via numerical methods before, but has never been attempted through an analytic approach, like in this paper. We prove the exponential decay of the solution in a one dimensional case and also discuss the limitations we face when we extend the problem to a system of equations posed on a finite disk.

Degree Name

Mathematics

Level of Degree

Doctoral

Department Name

Mathematics & Statistics

First Advisor

Lorenz, Jens

First Committee Member (Chair)

Stephen, La

Second Committee Member

Francesco, Sorrentino

Third Committee Member

Pereyra, M. Cristina

Language

English

Keywords

Rotating waves, Exponential decay, Reaction-diffusion system, Sobolev embedding, Contraction mapping

Document Type

Dissertation

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