Determination of a time-dependent coefficient in awave equation with unusual boundary condition

Tekin, İbrahim

doi:10.2298/fil1909653t

Cited by 7 publications

(5 citation statements)

References 18 publications

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“…In the case of

τ = 0

α = 1

, and

b = 0

, the homogeneous equation () with linear right‐hand side is well known in literature as wave equation. Direct and inverse problems (i.e., coefficient and source) for the wave equation with various boundary conditions are satisfactorily investigated in previous works 20–28 . Moreover, for this case, if the time derivative in Equation () is a fractional derivative with the order 0 < α < 1 and 1 < α < 2 , Equation () is called a fractional diffusion and diffusion‐wave equation.…”

Section: Introductionmentioning

confidence: 93%

Inverse problem for a nonlinear third order in time partial differential equation

Tekin

2021

Math Methods in App Sciences

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“…In the case of

τ = 0

α = 1

, and

b = 0

Section: Introductionmentioning

confidence: 93%

Inverse problem for a nonlinear third order in time partial differential equation

Tekin

2021

Math Methods in App Sciences

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“…The inverse problem for identifying time- and/or space-wise coefficients in the second-order hyperbolic equations have been studied in Bui (2003), Cannon and DuChateau (1983), Eskin (2017), Jiang et al. (2017), Hasanov and Romanov (2017), Huntul and Tamsir (2021a), Ramm and Rakesh (1991), Salazar (2013), Stefanov and Uhlmann (2013), Tekin (2019a) and Yamamoto (1995). However, adequate investigations of the inverse problems for the second-order hyperbolic equation have been studied, yet the studied on inverse problems for the pseudo-hyperbolic equations are insufficient.…”

Section: Introductionmentioning

confidence: 99%

Reconstruction of a potential coefficient in the Rayleigh–Love equation with non-classical boundary condition

Huntul

Tamsir

2022

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PurposeThe purpose of this paper is to reconstruct the potential numerically in the fourth-order Rayleigh–Love equation with boundary and nonclassical boundary conditions, from additional measurement.Design/methodology/approachAlthough, the aforesaid inverse identification problem is ill-posed but has a unique solution. The authors use the cubic B-spline (CBS) collocation and Tikhonov regularization techniques to discretize the direct problem and to obtain stable as well as accurate solutions, respectively. The stability, for the discretized system of the direct problem, is also carried out by means of the von Neumann method.FindingsThe acquired results demonstrate that accurate as well as stable solutions for the a(t) are accessed for λ∈ {10–8, 10–7, 10–6, 10–5}, when p ∈ {0.01%, 0.1%} for both linear and nonlinear potential coefficient a(t). The stability analysis shows that the discretized system of the direct problem is unconditionally stable.Research limitations/implicationsSince the noisy data are introduced, the investigation and analysis model real circumstances where the practical quantities are naturally infested with noise.Practical implicationsThe acquired results demonstrate that accurate as well as stable solutions for the a(t) are accessed for λ∈ {10–8, 10–7, 10–6, 10–5}, when p ∈ {0.01%, 0.1%} for both linear and nonlinear potential coefficient a(t). The stability analysis shows that the discretized system of the direct problem is unconditionally stable.Originality/valueThe potential term in the fourth-order Rayleigh–Love equation from additional measurement is reconstructed numerically, for the first time. The technique establishes that accurate, as well as stable solutions are obtained.

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“…parabolic and hyperbolic equations, respectively) PDEs are studied satisfactorily. The inverse problems of the parabolic and hyperbolic PDEs investigated numerically and/or theoretically in [10][11][12] and [13,14], respectively. The inverse problems of determining time or space dependent coefficients for the higher order in time (more than 2) PDEs attract many scientists.…”

Section: Introductionmentioning

confidence: 99%

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

Huntul¹,

Tekin²

2022

Bul. Kar. Univ. - Math.

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Derivatives in time of higher order (more than two) arise in various fields such as acoustics, medical ultrasound, viscoelasticity and thermoelasticity. The inverse problems for higher order derivatives in time equations connected with recovery of the coefficient are scarce and need additional consideration. In this article the inverse problem of determination is considered which depends on time, lowest term coefficient in differential equation in partial derivatives of fourth order in time with initial and boundary conditions from an additional integral observation is considered. Under some conditions regularity, consistency and orthogonality of data by using of the contraction principle the unique solvability of the solution of the coefficient identification problem on a sufficiently small time interval has been proved.

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Determination of a time-dependent coefficient in awave equation with unusual boundary condition

Cited by 7 publications

References 18 publications

Inverse problem for a nonlinear third order in time partial differential equation

Inverse problem for a nonlinear third order in time partial differential equation

Reconstruction of a potential coefficient in the Rayleigh–Love equation with non-classical boundary condition

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

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