We study the “finite extinction phenomenon” for solutions of parabolic reaction-diffusion equations of the type ∂u ∂t −∆u+ b(t)f(u(t− τ,x)) = 0, (t,x) ∈ (0,+∞)×Ω, with a delay term τ > 0. Here Ω is… (More)

We give sufficient conditions to have the finite extinction for all solutions of linear parabolic reaction-diffusion equations of the type ∂u ∂t − ∆u = −M(t)u(t − τ , x) (1) with a delay term τ > 0,… (More)

Global time-delay autosynchronization is known to control spatiotemporal turbulence in oscillatory reaction-diffusion systems. Here, we investigate the complex Ginzburg-Landau equation in the regime… (More)

We prove that the mere presence of a delayed term is able to connect the initial state u0 on a manifold without boundary (here assumed given as the set ∂Ω where Ω is an open bounded set in RN ) with… (More)

We consider the complex Ginzburg-Landau equation with feedback control given by some delayed linear terms (possibly dependent of the past spatial average of the solution). We prove several… (More)

Blow-up phenomena are analyzed for both the delay-differential equation (DDE) u(t) = B(t)u(t− τ), and the associated parabolic PDE (PDDE) ∂tu = ∆u+B (t)u(t− τ, x), where B : [0, τ ] → R is a positive… (More)

It is well known that several features of many reaction-diffusion systems can be studied through an associated Complex Ginzburg-Landau Equation (CGLE). In particular, the study of the catalytic CO… (More)

We show how to stabilize the uniform oscillations of the complex Ginzburg–Landau equation with periodic boundary conditions by means of some global delayed feedback. The proof is based on an abstract… (More)

Standing waves are studied as solutions of a complex Ginzburg-Landau equation subjected to local and global time-delay feedback terms. The onset is described as an instability of the uniform… (More)