# Journal of Dynamics and Differential Equations

Journal of Dynamics and Differential Equations > 2008 > 20 > 1 > 271-276

Journal of Dynamics and Differential Equations > 2008 > 20 > 1 > 201-238

Journal of Dynamics and Differential Equations > 2008 > 20 > 1 > 87-113

*f*(0) = 0, and λ

_{1}is exactly the first Dirichlet eigenvalue of −Δ in Ω. In this...

Journal of Dynamics and Differential Equations > 2008 > 20 > 1 > 31-53

Journal of Dynamics and Differential Equations > 2008 > 20 > 1 > 165-199

Journal of Dynamics and Differential Equations > 2008 > 20 > 1 > 133-164

Journal of Dynamics and Differential Equations > 2008 > 20 > 1 > 55-85

*J*

_{1}(

*t*) = α

*t*

^{ω}, with α > 0 and $$\omega > -\frac{1}{2}$$ . For this infinite dimensional system we prove solutions converge to similarity profiles as

*t*and

*j*converge to infinity in a similarity way, namely with either $$j\!/\!\varsigma$$ or $$(j-\varsigma)/\sqrt{\varsigma}$$...

Journal of Dynamics and Differential Equations > 2008 > 20 > 1 > 1-29

Journal of Dynamics and Differential Equations > 2008 > 20 > 1 > 115-132

**13**, 255–260, 1972) and Hunt

*et al*. (

*Bull. Am. Math. Soc*...

Journal of Dynamics and Differential Equations > 2008 > 20 > 1 > 239-270

Journal of Dynamics and Differential Equations > 2008 > 20 > 2 > 531-533

Journal of Dynamics and Differential Equations > 2008 > 20 > 2 > 301-335

*X*(

*t*,

*s*,

*x*) of a 2

*D*-Navier–Stokes equation subjected to a periodic time dependent forcing term. We prove in particular that as $${t \to \infty}$$ , $${\mathbb{E}[\varphi(X(t, s, x))]}$$ approaches a periodic orbit independently of

*s*and

*x*for any continuous and bounded real function $${\varphi}$$ .

Journal of Dynamics and Differential Equations > 2008 > 20 > 2 > 479-518

*P*

_{ m }be the projection onto the first

*m*eigenspaces of

*A*=−Δ, let μ and α be positive constants with α ≥3/2, and let

*Q*

_{ m }=

*I*−

*P*

_{ m }, then we add to the NSE operators μ...

Journal of Dynamics and Differential Equations > 2008 > 20 > 2 > 281-299

*nonuniform*exponential dichotomy, we show that there exist invariant stable manifolds as regular as the dynamics. We also consider the general case of a nonautonomous dynamics defined by the composition of a sequence of maps. The proof is based on a geometric argument that avoids any lengthy computations involving the higher order derivatives. In addition,...

Journal of Dynamics and Differential Equations > 2008 > 20 > 2 > 519-529

Journal of Dynamics and Differential Equations > 2008 > 20 > 2 > 425-477

Journal of Dynamics and Differential Equations > 2008 > 20 > 2 > 377-423

Journal of Dynamics and Differential Equations > 2008 > 20 > 2 > 337-376

Journal of Dynamics and Differential Equations > 2008 > 20 > 3 > 609-641