Length scales and positivity of solutions of a class of reaction-diffusion equations

MV Bartuccelli, KB Blyuss, Y Kyrychko

Research output: Contribution to journalArticle (Academic Journal)

2 Citations (Scopus)

Abstract

In this paper, the sharpest interpolation inequalities are used to find a set of length scales for the solutions of the following class of dissipative partial differential equations u(t) = -alpha(k) (-1)(k)del(2k)u + Sigma(j=1)(k-1) alpha(j)(-1)(j)del(2j)u + del(2)(u(m)) + u(1 - u(2p)), with periodic boundary conditions on a one-dimensional spatial domain. The equation generalises nonlinear diffusion model for the case when higher-order differential operators axe present. Furthermore, we establish the asymptotic positivity as well as the positivity of solutions for all times under certain restrictions on the initial data. The above class of equations reduces for some particular values of the parameters to classical models such as the KPP-Fisher equation which appear in various contexts in population dynamics.
Translated title of the contributionLength scales and positivity of solutions of a class of reaction-diffusion equations
Original languageEnglish
Pages (from-to)25 - 40
Number of pages16
JournalCommunications on Pure and Applied Analysis
Volume3 (1)
Publication statusPublished - Mar 2004

Bibliographical note

Publisher: American Institute of Mathematical Sciences

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