Remarks on contractions of reaction-diffusion PDE's on weighted L^2 norms

Zahra Aminzare

Back

Remarks on contractions of reaction-diffusion PDE's on weighted L^2 norms

Preprint

Open access

Remarks on contractions of reaction-diffusion PDE's on weighted L^2 norms

Zahra Aminzare

ArXiv.org

08/05/2012

Files and links (1)

url

https://arxiv.org/abs/1208.1045View

Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

In [1], we showed contractivity of reaction-diffusion PDE: \frac{\partial u}{\partial t}({\omega},t) = F(u({\omega},t)) + D\Delta u({\omega},t) with Neumann boundary condition, provided \mu_{p,Q}(J_F (u)) < 0 (uniformly on u), for some 1 \leq p \leq \infty and some positive, diagonal matrix Q, where J_F is the Jacobian matrix of F. This note extends the result for Q weighted L_2 norms, where Q is a positive, symmetric (not merely diagonal) matrix and Q^2D+DQ^2>0.

Details

Title: Subtitle: Remarks on contractions of reaction-diffusion PDE's on weighted L^2 norms
Creators: Zahra Aminzare
Resource Type: Preprint
Publication Details: ArXiv.org
ISSN: 2331-8422
Language: English
Date posted: 08/05/2012
Academic Unit: Mathematics; Iowa Neuroscience Institute
Record Identifier: 9984065884402771

Metrics

12 Record Views