Document Type
Report
Source Publication Title
Technical Report 138
Abstract
In the study of comparison theorems, existence of extremal solutions and monotone iterative techniques for differential systems a property called quasimonotone property is necessary [2,7,10]. However, there are several physical situations wherein such a property is not satisfied [1]. This difficulty has been overcome by introducing the notion of quasi-solutions [3,8,9]. In this paper we consider the reaction-diffusion system in which quasi-monotone property is not satisfied but a mixed quasimonotone property holds. By utilizing fruitfully the notion of quasi-solutions we prove the existence of coupled maximal and minimal solutions. For this purpose we exploit the monotone iterative technique. We then offer methods of constructing explicit coupled upper and lower solutions from which we deduce the asymptotic behaviour of solutions. Our results are in the spirit of similar results given in [1,5,10] and shed much light on the whole situation.
Disciplines
Mathematics | Physical Sciences and Mathematics
Publication Date
8-1-1980
Language
English
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Ladde, G. S.; Vatsala, A. S.; and Lakshmikantham, V., "Existence and Asymptotic Behavior of Reaction-Diffusion Systems Via Coupled Quasi-Solutions" (1980). Mathematics Technical Papers. 218.
https://mavmatrix.uta.edu/math_technicalpapers/218