In this survey we look at parabolic partial differential equations from a dynamical systems
point of view. With origins deeply rooted in celestial mechanics, and many modern aspects …

This survey is devoted to an introduction to the theory of global attractors for semigroups
defined on infinite dimensional spaces, which has mainly been developed in the last three …

State-of-the-art in qualitative theory of functional differential equations; Most of the new
material has never appeared in book form and some not even in papers; Second edition …

This book provides a comprehensive study of how attractors behave under perturbations for
both autonomous and non-autonomous problems. Furthermore, the forward asymptotics of …

In this work we study Morse–Smale semigroups under nonautonomous perturbations, which
leads us to introduce the concept of Morse–Smale evolution processes of hyperbolic type …

In this paper, we show that, for scalar reaction–diffusion equations ut= uxx+ f (x, u, ux) on the
circle S1, the Morse–Smale property is generic with respect to the non-linearity f. In Czaja …

In this paper we deal with Lipschitz continuous perturbations of gradient Morse-Smale
semigroups (all critical elements are equilibria). We study the permanence of connections …

We investigate heteroclinic orbits between equilibria and rotating waves for scalar
semilinear parabolic reaction-advection-diffusion equations with periodic boundary …

We prove that stable and unstable manifolds of hyperbolic periodic orbits for general scalar
reaction–diffusion equations on a circle always intersect transversally. The argument also …

We explicitly construct global attractors of fully nonlinear parabolic equations in one spatial
dimension. These attractors are decomposed as equilibria (time independent solutions) and …