In this review we discuss bifurcation theory in a Banach space setting using the singularity
theory developed by Golubitsky and Schaeffer to classify bifurcation points. The numerical …

This book describes the research that has been done on the problems of Benard convection-
as well as its modern offspring, the Rayleigh-Benard problem-and Taylor vortices. Benard …

We consider the effects of convection on chemical waves in which density gradients result
from the exothermicity as well as from the isothermal volumechange of the reaction. If the …

The article describes a complete numerical solution of a recently formulated benchmark
problem devoted to the parametric study of Rayleigh–Bénard instability in rectangular two …

Marangoni convection in a differentially heated binary mixture is studied numerically by
continuation. The fluid is subject to the Soret effect and is contained in a two-dimensional …

In the present study, we focus on the computational analysis of partial differential equations
with emphasis on the stability of the equilibrium states and on their bifurcations. In practical …

This work addresses the stability of a two-dimensional plane layer of a dielectric liquid
enclosed in wall bounded cavities of different aspect ratios and subjected to unipolar …

Thermocapillary convection arising in small-depth layers (long horizontal cavities) subject to
a horizontal temperature gradient is studied numerically. A broad range of values of the …

Double-diffusive Marangoni convection in a rectangular cavity with horizontal temperature
and concentration gradients is considered. Attention is restricted to the case where the …

We investigate the linear stability threshold of a dielectric liquid subjected to unipolar
injection in a two-dimensional rectangular enclosure with rigid boundaries. A finite element …