The Galerkin Method for Fourth-Order Equation of the Moore–Gibson–Thompson Type with Integral Condition

Abstract

In this manuscript, we consider the fourth order of the Moore–Gibson–Thompson equation by using Galerkin’s method to prove the solvability of the given nonlocal problem.

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

“…After some manipulations in last equations under the assumptions (A 1 )-(A 6 ) and using the estimates ( 17)- (18) , we obtain…”

“…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].…”

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

“…where f int (τ ) = 1 0 f (x, τ )dx. If we consider u n (τ ) which is defined in (8) and its second derivative into the last equation, we get…”

“…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].…”