Spatial Decay of Rotating Waves and Restrictions on Finite Disks.

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.

Name thesis:degree_name

Mathematics

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics & Statistics

Year

2015

Author dc:creator

• Konda, Sahitya

Contributors dc:contributor

• Lorenz, Jens
• Jens Lorenz
• Stephen Lau
• Maria Cristina Pereyra
• Francesco Sorrentino

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

Language dc:language

English

Identifier

https://digitalrepository.unm.edu/math_etds/24

OAI identifier oai:identifier

oai:digitalrepository.unm.edu:math_etds-1023