Well-posedness for a fourth-order equation of Moore–Gibson–Thompson type

Abstract

In this paper, we completely characterize, only in terms of the data, the well-posedness of a fourth order abstract evolution equation arising from the Moore–Gibson–Thomson equation with memory. This characterization is obtained in the scales of vector-valued Lebesgue, Besov and Triebel–Lizorkin function spaces. Our characterization is flexible enough to admite as examples the Laplacian and the fractional Laplacian operators, among others. We also provide a practical and general criteria that allows Lp–Lq-well posedness.

Identification of the time-dependent lowest term in a fourth order in time partial differential equation

“…This model is obtained from the third-order Moore-Gibson-Thompson equation with memory, which has been extensively studied in the literature, [7,13,14]. More recently, this model has attracted the attention of many authors, see [3,15,16,18,19].…”

Well‐posedness for the fourth‐order Moore–Gibson–Thompson equation in the class of Banach‐space‐valued Hölder‐continuous functions

“…In a previous study, 15 Liu et al continued this analysis incorporating a delay memory term in the model and stated general decay results. More recently, in another study, 16 Lizama and Murillo-Arcila characterized the well-posedness of (1.1) in the scales of vector-valued Lebesgue, Besov, and Triebel Lizorkin function spaces.…”

Inverse coefficient problem for differential equation in partial derivatives of a fourth order in time with integral over-determination

“…The fourth order in time equation, that is our motivation point, was introduced and first studied by Dell'Oro and Pata [4] ∂ τ τ τ τ u(x, τ ) + α∂ τ τ τ u(x, τ ) + β∂ τ τ u(x, τ ) − γ ∂ τ τ u(x, τ ) − ρ u(x, τ ) = 0, where α, β, γ, ρ are real numbers. More recently, this model has attracted the attention of many authors, [5][6][7][8][9].…”