The paper deals with local well-posedness, global existence and blow-up results for reaction-diffusion equations coupled with nonlinear dynamical boundary conditions. The typical problem studied is - ut - Δu = up-2 u in (0;∞) ; u = 0 on [0; ∞) × ωu =0 = um -2 ut on [0; ∞) 1; u (0; x) = u0 (x) in where is a bounded open regular domain of Rn (n ≥ 1), = 0 [ 1, 2 ≤ p 1+2=2, m 1 and u0 2 H1(), u0 0 = 0. After showing local well-posedness in the Hadamard sense we give global existence and blow-up results when 0 has positive surface measure. Moreover we discuss the generalization of the above mentioned results to more general problems where the terms u p -2u and ut m-2ut are respectively replaced by f (x; u) and Q(t; x; ut) under suitable assumptions on them.

Fiscella, A., Vitillaro, E. (2013). Local Hadamard well-posedness and blow-up for reaction-diffusion equations with non-linear dynamical boundary conditions. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 33(11-12), 5015-5047 [10.3934/dcds.2013.33.5015].

Local Hadamard well-posedness and blow-up for reaction-diffusion equations with non-linear dynamical boundary conditions

Fiscella A
;
2013

Abstract

The paper deals with local well-posedness, global existence and blow-up results for reaction-diffusion equations coupled with nonlinear dynamical boundary conditions. The typical problem studied is - ut - Δu = up-2 u in (0;∞) ; u = 0 on [0; ∞) × ωu =0 = um -2 ut on [0; ∞) 1; u (0; x) = u0 (x) in where is a bounded open regular domain of Rn (n ≥ 1), = 0 [ 1, 2 ≤ p 1+2=2, m 1 and u0 2 H1(), u0 0 = 0. After showing local well-posedness in the Hadamard sense we give global existence and blow-up results when 0 has positive surface measure. Moreover we discuss the generalization of the above mentioned results to more general problems where the terms u p -2u and ut m-2ut are respectively replaced by f (x; u) and Q(t; x; ut) under suitable assumptions on them.
Articolo in rivista - Articolo scientifico
heat equation, dynamical boundary conditions, reaction diffusion, equations, blow-up, Hadamard well-posedness
English
5015
5047
33
Hybrid Gold Open Access• Green Open Access
Fiscella, A., Vitillaro, E. (2013). Local Hadamard well-posedness and blow-up for reaction-diffusion equations with non-linear dynamical boundary conditions. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 33(11-12), 5015-5047 [10.3934/dcds.2013.33.5015].
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/338118
Citazioni
  • Scopus 7
  • ???jsp.display-item.citation.isi??? 6
Social impact