B. Fiedler, C. Grotta-Ragazzo, C. Rocha, “An explicit Lyapunov function for reflection symmetric parabolic partial differential equations on the circle”, Uspekhi Mat. Nauk, 2014, Volume 69, Issue 3(417),Pages <nobr>27

This article is cited in 12 papers

An explicit Lyapunov function for reflection symmetric parabolic partial differential equations on the circle

B. Fiedler^a, C. Grotta-Ragazzo^b, C. Rocha^c

^a Institut für Mathematik, Freie Universität Berlin, Berlin, Germany
^b Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, Brazil
^c Instituto Superior Técnico, Lisboa, Portugal

Abstract: An explicit Lyapunov function is constructed for scalar parabolic reaction-advection-diffusion equations under periodic boundary conditions. The non-linearity is assumed to be even with respect to the advection term. The method followed was originally suggested by H. Matano for, and limited to, separated boundary conditions.
Bibliography: 20 titles.

Keywords: partial differential equations, variational methods, convection, energy functional, advection, reaction-diffusion equations, periodic boundary conditions.

UDC: 517.956.4

MSC: 35B40, 35K55

Received: 25.10.2013

DOI: 10.4213/rm9591