We systematically explore a simple class of global attractors, called Sturm due to nodal
properties, for the semilinear scalar parabolic partial differential equation (PDE) ut= ux x+ f …

Lyapunov functions are used in order to prove stability of equilibria, or to indicate a gradient-
like structure of a dynamical system. Zelenyak (1968) and Matano (1988) constructed a …

The goal of this paper is to construct explicitly the global attractors of parabolic equations
with singular diffusion coefficients on the boundary, as it was done without the singular term …

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

In this work, we present results on stability and hyperbolicity of equilibria for a scalar
nonlocal one-dimensional quasilinear parabolic problem. We show that this nonlocal …

In this article, we study the structure of the global attractor for a non-local one-dimensional
quasilinear problem. The strong relation of our problem with a non-local version of the …

Dynamical systems generated by scalar reaction-diffusion equations on an interval enjoy
special properties that lead to a very simple structure for the semiflow. Among these …

In this paper, we develop first a theory of existence of index pairs for multivalued semiflows.
We apply this result to a reaction-diffusion equation having a discontinuous nonlinearity …

The goal of this paper is to construct explicitly the global attractors of semilinear parabolic
equations when the reaction term has an oscillating growth. In this case, solution can also …

The Einstein constraint equations describe the space of initial data for the evolution
equations, dictating how space should curve within spacetime. Under certain assumptions …