Exponential Decay Results for Semilinear Parabolic PDE with $C^0$ Potentials: A "Mean Value" Approach
Analysis of PDEs
2016-01-15 v2
Abstract
The asymptotic behavior of some semilinear parabolic PDEs is analyzed by means of a "mean value" property. This property allows us to determine, by means of appropriate {\em{a priori}} estimates, some exponential decay results for suitable global solutions. We also apply the method to investigate a well-known finite time blow-up result. An application is given to a one-dimensional semilinear parabolic PDE with boundary degeneracy. Our results shed further light onto the problem of determining initial data for which the corresponding solution is guaranteed to exponentially decay to zero or blow-up in finite time.
Keywords
Cite
@article{arxiv.1406.3271,
title = {Exponential Decay Results for Semilinear Parabolic PDE with $C^0$ Potentials: A "Mean Value" Approach},
author = {Joseph L. Shomberg},
journal= {arXiv preprint arXiv:1406.3271},
year = {2016}
}
Comments
15 pages, 3 figures; to appear in Differential Equations and Dynamical Systems