We consider the MGT equation with memory ∂tttu + α ∂ttu - β∆ ∂tu - γ∆u +Z0t g(s)∆u(t - s)ds = 0. We prove an existence and uniqueness result removing the convexity assumption on the convolution kernel g, usually adopted in the literature. In the subcritical case αβ > γ, we establish the exponential decay of the energy, without leaning on the classical differential inequality involving g and its derivative g′, namely, g′ + δg ≤ 0, δ > 0, but we ask only that g vanish exponentially fast.

Conti, M., Liverani, L., Pata, V. (2023). On the Moore-Gibson-Thompson Equation with Memory with Nonconvex Kernels. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 72(1), 1-27 [10.1512/iumj.2023.72.9330].

On the Moore-Gibson-Thompson Equation with Memory with Nonconvex Kernels

Liverani L.
Co-primo
;
2023

Abstract

We consider the MGT equation with memory ∂tttu + α ∂ttu - β∆ ∂tu - γ∆u +Z0t g(s)∆u(t - s)ds = 0. We prove an existence and uniqueness result removing the convexity assumption on the convolution kernel g, usually adopted in the literature. In the subcritical case αβ > γ, we establish the exponential decay of the energy, without leaning on the classical differential inequality involving g and its derivative g′, namely, g′ + δg ≤ 0, δ > 0, but we ask only that g vanish exponentially fast.
Articolo in rivista - Articolo scientifico
existence and uniqueness of solutions; exponential decay of the energy; MGT equation with memory; nonconvex memory kernel;
English
2023
72
1
1
27
open
Conti, M., Liverani, L., Pata, V. (2023). On the Moore-Gibson-Thompson Equation with Memory with Nonconvex Kernels. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 72(1), 1-27 [10.1512/iumj.2023.72.9330].
File in questo prodotto:
File Dimensione Formato  
Conti-2023-Indiana Univ Math J-preprint.pdf

accesso aperto

Descrizione: Article
Tipologia di allegato: Submitted Version (Pre-print)
Licenza: Creative Commons
Dimensione 310.75 kB
Formato Adobe PDF
310.75 kB Adobe PDF Visualizza/Apri

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/10281/414596
Citazioni
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 4
Social impact