LARGE-TIME ASYMPTOTICS OF THE REGULARIZED MOORE-GIBSON-THOMPSON EQUATION WITH GURTIN-PIPKIN THERMAL LAW

Primio AD, Liverani L (2026)

Publication Type: Journal article

Publication year: 2026

Journal

Discrete and Continuous Dynamical Systems. Series S American Institute of Mathematical Sciences (AIMS)

Pages Range: 1-27

DOI: 10.3934/DCDSS.2026054

Abstract

We study the system of linear PDEs (Formula Presented) constituted by a regularized Moore-Gibson-Thompson (MGT) equation, coupled to the Gurtin-Pipkin thermal law. Here α, β, γ and δ are positive constant parameters, while g is a positive, convex, and summable memory kernel. Within the regularized MGT-subcritical regime (Formula Presented) where λ0 is the first eigenvalue of −∆, we show that the system generates an exponentially stable semigroup. Instead, in the critical regime κδ = 0, we prove that there exist kernels g(s), called resonant, for which the system admits periodic trajectories. We conclude with a numerical exploration of the case of general kernels, showing evidence that, aside from resonant kernels, the semigroup generated by the system is expected to be exponentially stable even in the critical regime.

Authors with CRIS profile

Lorenzo Liverani Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Involved external institutions

Scuola Normale Superiore di Pisa (SNS)

Italy (IT)

How to cite

APA:

Primio, A.D., & Liverani, L. (2026). LARGE-TIME ASYMPTOTICS OF THE REGULARIZED MOORE-GIBSON-THOMPSON EQUATION WITH GURTIN-PIPKIN THERMAL LAW. Discrete and Continuous Dynamical Systems. Series S, 1-27. https://doi.org/10.3934/DCDSS.2026054

MLA:

Primio, Andrea Di, and Lorenzo Liverani. "LARGE-TIME ASYMPTOTICS OF THE REGULARIZED MOORE-GIBSON-THOMPSON EQUATION WITH GURTIN-PIPKIN THERMAL LAW." Discrete and Continuous Dynamical Systems. Series S (2026): 1-27.

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