On admissibility for parabolic equations in ℝⁿ

• Autorzy: Martino Prizzi
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 35K57: Reaction-diffusion equations
• 35J60: Nonlinear elliptic equations
• 37B30: Index theory, Morse-Conley indices

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2003
• Tom: 176
• Numer: 3
• Strony: 261-275

Daty

wydano

2003

Twórcy

autor

Martino Prizzi

• Dipartimento di Scienze Matematiche, Università degli Studi di Trieste, via Valerio 12, 34127 Trieste, Italy

Identyfikatory

DOI

10.4064/fm176-3-5