Curved thin domains and parabolic equations

M. Prizzi; M. Rinaldi; K. P. Rybakowski

doi:10.4064/sm151-2-2

Curved thin domains and parabolic equations

M. Prizzi, M. Rinaldi, K. P. Rybakowski

Risultato della ricerca: Contributo su rivista › Articolo in rivista › peer review

Abstract

Consider the family u_t = Δu + G(u), t > 0, x ∈ Ω_ε (E_ε) ∂_νε u = 0, t > O, x ∈ ∂ Ω_ε of semilinear Neumann boundary value problems, where, for ε > 0 small, the set Ω_ε is a thin domain in ℝ^l, possibly with holes, which collapses, as ε → 0⁺, onto a (curved) k-dimensional submanifold of ℝ^l. If G is dissipative, then equation (E_epsi;) has a global attractor A_ε. We identify a "limit" equation for the family (E_ε), prove convergence of trajectories and establish an upper semicontinuity result for the family A_ε as ε → 0⁺.

Lingua originale	Inglese
pagine (da-a)	109-140
Numero di pagine	32
Rivista	Studia Mathematica
Volume	151
Numero di pubblicazione	2
DOI	https://doi.org/10.4064/sm151-2-2
Stato di pubblicazione	Pubblicato - 2002
Pubblicato esternamente	Sì

Accesso al documento

10.4064/sm151-2-2

Altri file e collegamenti

Link to publication in Scopus

Cita questo

@article{ab123a5983e14ef1a02c5241158a8d2f,

title = "Curved thin domains and parabolic equations",

abstract = "Consider the family ut = Δu + G(u), t > 0, x ∈ Ωε (Eε) ∂νε u = 0, t > O, x ∈ ∂ Ωε of semilinear Neumann boundary value problems, where, for ε > 0 small, the set Ωε is a thin domain in ℝl, possibly with holes, which collapses, as ε → 0+, onto a (curved) k-dimensional submanifold of ℝl. If G is dissipative, then equation (Eepsi;) has a global attractor Aε. We identify a {"}limit{"} equation for the family (Eε), prove convergence of trajectories and establish an upper semicontinuity result for the family Aε as ε → 0+.",

keywords = "Attractors, Curved squeezed domains, Reaction-diffusion equations",

author = "M. Prizzi and M. Rinaldi and Rybakowski, \{K. P.\}",

year = "2002",

doi = "10.4064/sm151-2-2",

language = "English",

volume = "151",

pages = "109--140",

journal = "Studia Mathematica",

issn = "0039-3223",

publisher = "Institute of Mathematics, Polish Academy of Sciences",

number = "2",

}

TY - JOUR

T1 - Curved thin domains and parabolic equations

AU - Prizzi, M.

AU - Rinaldi, M.

AU - Rybakowski, K. P.

PY - 2002

Y1 - 2002

N2 - Consider the family ut = Δu + G(u), t > 0, x ∈ Ωε (Eε) ∂νε u = 0, t > O, x ∈ ∂ Ωε of semilinear Neumann boundary value problems, where, for ε > 0 small, the set Ωε is a thin domain in ℝl, possibly with holes, which collapses, as ε → 0+, onto a (curved) k-dimensional submanifold of ℝl. If G is dissipative, then equation (Eepsi;) has a global attractor Aε. We identify a "limit" equation for the family (Eε), prove convergence of trajectories and establish an upper semicontinuity result for the family Aε as ε → 0+.

AB - Consider the family ut = Δu + G(u), t > 0, x ∈ Ωε (Eε) ∂νε u = 0, t > O, x ∈ ∂ Ωε of semilinear Neumann boundary value problems, where, for ε > 0 small, the set Ωε is a thin domain in ℝl, possibly with holes, which collapses, as ε → 0+, onto a (curved) k-dimensional submanifold of ℝl. If G is dissipative, then equation (Eepsi;) has a global attractor Aε. We identify a "limit" equation for the family (Eε), prove convergence of trajectories and establish an upper semicontinuity result for the family Aε as ε → 0+.

KW - Attractors

KW - Curved squeezed domains

KW - Reaction-diffusion equations

UR - https://www.scopus.com/pages/publications/0036324731

U2 - 10.4064/sm151-2-2

DO - 10.4064/sm151-2-2

M3 - Article

SN - 0039-3223

VL - 151

SP - 109

EP - 140

JO - Studia Mathematica

JF - Studia Mathematica

IS - 2

ER -

Curved thin domains and parabolic equations

Abstract

Accesso al documento

Altri file e collegamenti

Fingerprint

Cita questo