Determination of parameters in telegraph equation

Abstract

Abstract. We study the solvability of the inverse problems on finding a solution ( , ) and an unknown coefficient for a telegraph equationWe prove the theorems on the existence of the regular solutions. The feature of the problems is a presence of new overdetermination conditions for the considered class of equations.

Hyperbolic Equations with Unknown Coefficients

“…Finally, estimates ( 33) and ( 34) together with (29) give the following inequality for the solutions u(x, t) to the boundary value problem (1 ), (2)-( 4):…”

“…As for inverse problems with unknown constant coefficients for hyperbolic equations, we can only mention [29], where the inverse problem was studied for finding the lower coefficient in a telegraph equation, and here the quadratic final-integral overdetermination condition was used.…”

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

“…SIPs for partial differential equations (DEs) play a significant role in natural science, applied sciences, engineering, quantum mechanics, diffusion equations, and heat equations (see, e.g., [1][2][3][4]). The study of space-dependent and time-dependent source identification iproblems for partial DEs plays a significant role in engineering and applied sciences (e.g., communication, machines and buildings, mathematical physics, and chemical physics) and has been investigated by many authors [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. In [5], the singular boundary method was applied to solve the mixed problem.…”

“…In addition, in [43], the authors investigated the source identification problems for the elliptic-telegraph differential equation with unknown parameter P in a Hilbert space with a self-adjoint positive definite operator. In [11], Kozhanov and Safiullaeva studied the solvability of the inverse problems on finding a solution W(τ, η) and an unknown coefficient c for a TDE…”

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

“…The telegraph hyperbolic partial differential equation is important for modeling several relevant problems such as in signal analysis, wave propagation, random walk theory [19], [20], [21], [22], [23], [24], [25], [26]. To deal with this equation, various mathematical methods have been proposed for obtaining exact and approximate analytic solutions.…”