Uniqueness criterion in an inverse problem for an abstract differential equation with nonstationary inhomogeneous term

Tikhonov, I. V.; Eidelman, Yuli

doi:10.1007/s11006-005-0024-0

Cited by 15 publications

(13 citation statements)

References 2 publications

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“…To find a review of publications about inverse problems for Eq. (1.4) with various assumptions regarding the operator A, see [4,5,12,14,15].…”

Section: Problem Posingmentioning

confidence: 99%

“…In the above papers [4,5,12,14,15] devoted to the inverse problem for Eq. (1.4), the case where A is a generator of an IS is not considered.…”

Section: Inverse Problems With Stationary Inhomogeneous Termsmentioning

confidence: 99%

“…The case where γ = β = 0 and A is a generator of a C 0 -semigroup is well-known from [4,5,12,14,15]; it is a "limiting" case for problem (3.1)- (3.3). The case where γ = 1 and β > 0 is covered by Theorem 2. where λ ∈ ρ(A) and Re λ > σ > ω.…”

Section: Inverse Problems With Stationary Inhomogeneous Termsmentioning

confidence: 99%

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Inverse problems for evolution equations with fractional integrals at boundary-value conditions

Glushak¹

2010

J Math Sci

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“…To find a review of publications about inverse problems for Eq. (1.4) with various assumptions regarding the operator A, see [4,5,12,14,15].…”

Section: Problem Posingmentioning

confidence: 99%

“…In the above papers [4,5,12,14,15] devoted to the inverse problem for Eq. (1.4), the case where A is a generator of an IS is not considered.…”

Section: Inverse Problems With Stationary Inhomogeneous Termsmentioning

confidence: 99%

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Inverse problems for evolution equations with fractional integrals at boundary-value conditions

Glushak¹

2010

J Math Sci

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“…The authors usually set an additional condition (1.2) at the final time t 0 = T (see, e.g. [6], [7] for classical diffusion equations and for subdiffusion equations see [8], [9]). The meaning of taking condition (1.2) at t 0 is that in some cases the uniqueness of the solution of the inverse problem is violated if t 0 = T and by choosing t 0 it is possible to achieve uniqueness in these cases as well.…”

Section: Introductionmentioning

confidence: 99%

Inverse problem for the subdiffusion equation with fractional Caputo derivative

Ashurov¹,

Marjona²

2022

Preprint

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The inverse problem of determining the right-hand side of the subdiffusion equation with the fractional Caputo derivative is considered. The right-hand side of the equation has the form f (x)g(t) and the unknown is function f (x). The condition u(x, t 0 ) = ψ(x) is taken as the over-determination condition, where t 0 is some interior point of the considering domain and ψ(x) is a given function. It is proved by the Fourier method that under certain conditions on the functions g(t) and ψ(x) the solution of the inverse problem exists and is unique. An example is given showing the violation of the uniqueness of the solution of the inverse problem for some sign-changing functions g(t). It is shown that for the existence of a solution to the inverse problem for such functions g(t), certain orthogonality conditions for the given functions and some eigenfunctions of the elliptic part of the equation must be satisfied.

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“…For certain integral equations of convoluted form [3,4] the solutions depends on the singularities appearing by Laplace transforming [5]. Great interest is also devoted to the study of the zeros of entire and special functions with the most various applications, from relaxation-oscillation to fractional diffusion phenomena, to name a few [6,7,8,9,10,11,12,13,14,15].…”

Section: Introductionmentioning

confidence: 99%

Some transcendental equations on the Stieltjes cone

Giraldi¹

2015

Preprint

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A general class of transcendental equations in complex domain is considered for functions belonging to the Stieltjes cone. Under certain conditions each transcendental equation has no solution or one, at most, in the complex plane cut along the negative real axis. The unique solution is real valued and positive with an analytical bound. Particular cases consist in transcendental equations containing exponential, hyperbolic, power law, logarithmic and special functions. The present approach provides a simple way to prove that some special functions have no zero in certain sectors of the complex plane cut along the negative real axis.

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Uniqueness criterion in an inverse problem for an abstract differential equation with nonstationary inhomogeneous term

Cited by 15 publications

References 2 publications

Inverse problems for evolution equations with fractional integrals at boundary-value conditions

Inverse problems for evolution equations with fractional integrals at boundary-value conditions

Inverse problem for the subdiffusion equation with fractional Caputo derivative

Some transcendental equations on the Stieltjes cone

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