Local well-posedness for a class of semilinear Moore-Gibson-Thompson equations with subcritical nonlinearities

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Auteurs principaux: Bezerra, Flank D. M., Salge, Luís M.
Format: Preprint
Publié: 2025
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author Bezerra, Flank D. M.
Salge, Luís M.
author_facet Bezerra, Flank D. M.
Salge, Luís M.
contents In this paper, we study a class of higher-order semilinear evolution equations inspired by the Moore-Gibson-Thompson model introduced by Dell'Oro, Liverani and Pata (2023), involving strongly elliptic operators of order ($2m$) with homogeneous boundary conditions. The associated unbounded linear operator is a sectorial operator with zero belonging to the resolvent set, allowing the construction of fractional powers spaces, and the analysis of their spectral properties. We prove the local well-posedness of the corresponding semilinear Cauchy problem under subcritical nonlinearities. Our framework clarifies the role of extrapolation spaces and fractional domains in handling the lack of accretivity and bounded imaginary powers of the operator.
format Preprint
id arxiv_https___arxiv_org_abs_2510_06944
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Local well-posedness for a class of semilinear Moore-Gibson-Thompson equations with subcritical nonlinearities
Bezerra, Flank D. M.
Salge, Luís M.
Dynamical Systems
Analysis of PDEs
Functional Analysis
35G10, 35K46, 47A75, 47D03
In this paper, we study a class of higher-order semilinear evolution equations inspired by the Moore-Gibson-Thompson model introduced by Dell'Oro, Liverani and Pata (2023), involving strongly elliptic operators of order ($2m$) with homogeneous boundary conditions. The associated unbounded linear operator is a sectorial operator with zero belonging to the resolvent set, allowing the construction of fractional powers spaces, and the analysis of their spectral properties. We prove the local well-posedness of the corresponding semilinear Cauchy problem under subcritical nonlinearities. Our framework clarifies the role of extrapolation spaces and fractional domains in handling the lack of accretivity and bounded imaginary powers of the operator.
title Local well-posedness for a class of semilinear Moore-Gibson-Thompson equations with subcritical nonlinearities
topic Dynamical Systems
Analysis of PDEs
Functional Analysis
35G10, 35K46, 47A75, 47D03
url https://arxiv.org/abs/2510.06944