On admissibility for parabolic equations in ℝⁿ

Martino Prizzi. "On admissibility for parabolic equations in ℝⁿ." Fundamenta Mathematicae 176.3 (2003): 261-275. <http://eudml.org/doc/283277>.

@article{MartinoPrizzi2003,
abstract = {We consider the parabolic equation (P) $u_t - Δu = F(x,u)$, (t,x) ∈ ℝ₊ × ℝⁿ, and the corresponding semiflow π in the phase space H¹. We give conditions on the nonlinearity F(x,u), ensuring that all bounded sets of H¹ are π-admissible in the sense of Rybakowski. If F(x,u) is asymptotically linear, under appropriate non-resonance conditions, we use Conley’s index theory to prove the existence of nontrivial equilibria of (P) and of heteroclinic trajectories joining some of these equilibria. The results obtained extend earlier results of Rybakowski concerning parabolic equations on bounded open subsets of ℝⁿ.},
author = {Martino Prizzi},
journal = {Fundamenta Mathematicae},
keywords = {Conley index; admissibility; asymptotically linear parabolic equation},
language = {eng},
number = {3},
pages = {261-275},
title = {On admissibility for parabolic equations in ℝⁿ},
url = {http://eudml.org/doc/283277},
volume = {176},
year = {2003},
}

TY - JOUR
AU - Martino Prizzi
TI - On admissibility for parabolic equations in ℝⁿ
JO - Fundamenta Mathematicae
PY - 2003
VL - 176
IS - 3
SP - 261
EP - 275
AB - We consider the parabolic equation (P) $u_t - Δu = F(x,u)$, (t,x) ∈ ℝ₊ × ℝⁿ, and the corresponding semiflow π in the phase space H¹. We give conditions on the nonlinearity F(x,u), ensuring that all bounded sets of H¹ are π-admissible in the sense of Rybakowski. If F(x,u) is asymptotically linear, under appropriate non-resonance conditions, we use Conley’s index theory to prove the existence of nontrivial equilibria of (P) and of heteroclinic trajectories joining some of these equilibria. The results obtained extend earlier results of Rybakowski concerning parabolic equations on bounded open subsets of ℝⁿ.
LA - eng
KW - Conley index; admissibility; asymptotically linear parabolic equation
UR - http://eudml.org/doc/283277
ER -