Stability of the Time-Dependent Identification Problem for the Telegraph Equation With Involution

Abstract

In the present paper, a time-dependent source identification problem for a one dimensional telegraph equation with involution is studied. Theorems on the stability estimates for the solution of this problem are established.

Construction of Eigenfunctions to One Nonlocal Second-Order Differential Operator with Double Involution

“…Taking into account equality (5), from Theorem 1, this implies the equality of matrices (8). This proves the corollary.…”

“…Refs. [4][5][6][7][8][9][10][11][12][13][14][15] are devoted to the questions of solvability of boundary and initial-boundary value problems for differential equations with involution. Spectral questions of differential equations with involution are studied in [16][17][18][19][20][21][22][23][24][25].…”

An Operator Method for Investigation of the Stability of Time-Dependent Source Identification Telegraph Type Differential Problems

“…is satisfied for the isolution of IVP (9) for every τ, τ ∈ [0, Λ]. From iestimate (28), it follows estimate (25). Theorem 4 is proved.…”

“…for a one dimensional telegraph equation with involution and Neumann conditions was studied in paper [25]. Assume that all compatibility conditions for the given smooth data ifunctions F(τ, iη), a(η), (η), χ(η), ξ(τ), G(η) are fulfilled, that G (−b) = G (b) = 0 and a ≥ a(η) = a(−η) ≥ δ > 0, β > 0, δ − a|γ| ≥ 0,, and that b −b G(y)dy = 0.…”

Stability of the time-dependent identification problem for a fractional Telegraph equation with the Caputo derivative

“…To solve this time-dependent source identification problem one needs an extra condition. Following the paper of A. Ashyralyev et al see, [2] we consider the additional condition in a rather general form:…”