TITLE:
Stationary Solutions of a Mathematical Model for Formation of Coral Patterns
AUTHORS:
Lekam Watte Somathilake, Janak R. Wedagedera
KEYWORDS:
Reaction-Diffusion Equations, Stationary Solutions, Priori Estimates, Topological Degree Theory
JOURNAL NAME:
Applied Mathematics,
Vol.6 No.6,
June
10,
2015
ABSTRACT: A reaction-diffusion type mathematical model for growth of corals in a tank is considered. In this paper, we study stationary problem of the model subject to the homogeneous Neumann boundary conditions. We derive some existence results of the non-constant solutions of the stationary problem based on Priori estimations and Topological Degree theory. The existence of non-constant stationary solutions implies the existence of spatially variant time invariant solutions for the model.