Introduction:
Application of reaction diffusion models is seemingly endless with their use naturally arising in disciplines such as biology, ecology, chemistry, geology, physics, and engineering. Reaction diffusion models have recently become even more useful in modeling physical and biological phenomena due to many important developments in the study of their dynamics. A key tool in understanding the dynamics of such models requires detailed investigation of the structure solutions to the corresponding parabolic and elliptic partial differential equations. This investigation yields interesting nonlinear initialboundary and boundary value problems of varied types. Even though the study of reaction diffusion models has had a rich mathematical history dating back to the 1960’s, much is still not known about the structure of solutions to such problems. Several techniques have been developed and successfully used to solve these problems including, iterative monotone methods, subsuper solutions, topological degree theory, and variational methods, among others. 
