Document Type
Report
Source Publication Title
Technical Report 78
Abstract
In this paper we investigate the theory of parabolic differential inequalities in arbitrary cones. After discussing the fundamental results concerning parabolic inequalities in cones, we prove a result on flow-invariance which is then used to obtain a comparison theorem. This comparison result is useful in deriving upper and lower bounds on solutions of parabolic differential equations in terms of the solutions of ordinary differential equations. We treat the Dirichlet problem in this paper since its theory follows the general pattern of ordinary differential equations and requires less restrictive assumptions. The treatment of Neumann problem, on the other hand, demands stronger smoothness assumptions and depends heavily on strong maximum principle. The study of the corresponding results relative to Newmann problem is discussed elsewhere.
Disciplines
Mathematics | Physical Sciences and Mathematics
Publication Date
3-1-1978
Language
English
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Vaughn, Randy and Lakshmikantham, V., "Parabolic Differential Inequalities in Cones" (1978). Mathematics Technical Papers. 25.
https://mavmatrix.uta.edu/math_technicalpapers/25