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

Abstract

In this work, we provide a full characterization of well‐posedness in vector‐valued Hölder continuous function spaces for a fourth‐order abstract evolution equation arising from the Moore–Gibson–Thompson equation with memory using operator‐valued Ċα$$ {\dot{C}}^{\alpha } $$‐Fourier multipliers. We illustrate our results by providing an example based on the fourth order Moore–Gibson–Thompson equation with Dirichlet boundary conditions.

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

“…is the solution of the system of differential equations (7). Analogously, we can prove that if {u(x, τ ), a(τ )} is a solution of the inverse problem (1)-( 4), then u n (τ ), n = 0, 1, 2, ...satisfy the system of differential equations (7). For proof of this assertion please see [18].…”

“…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].…”

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].…”