Uniqueness for an inverse source problem of determining a space dependent source in a time-fractional diffusion equation

Slodička, Marián; Šišková, Katarína; Bockstal, Karel Van

doi:10.1016/j.aml.2018.11.012

Cited by 40 publications

(36 citation statements)

References 16 publications

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“…The ISP for missing f (x) has the trivial solution (T(x, t), f (x)) = (0, 0). We now determine a non-trivial solution, based on a modification of [23] Example 3.1. Take a function g(x) such that −∆g = λg with g(0) = g(π) = 0 and let v ∈ C 2 (0, 1) with v(0…”

Section: Uniqueness For Isp By Determination Of F(x) From the Final Time Observationmentioning

confidence: 99%

Some Inverse Source Problems of Determining a Space Dependent Source in Fractional-Dual-Phase-Lag Type Equations

Maes

Slodička

2020

Mathematics

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The dual-phase-lag heat transfer models attract a lot of interest of researchers in the last few decades. These are used in problems arising from non-classical thermal models, which are based on a non-Fourier type law. We study uniqueness of solutions to some inverse source problems for fractional partial differential equations of the Dual-Phase-Lag type. The source term is supposed to be of the form h(t)f(x) with a known function h(t). The unknown space dependent source f(x) is determined from the final time observation. New uniqueness results are formulated in Theorem 1 (for a general fractional Jeffrey-type model). Here, the variational approach was used. Theorem 2 derives uniqueness results under weaker assumptions on h(t) (monotonically increasing character of h(t) was removed) in a case of dominant parabolic behavior. The proof technique was based on spectral analysis. Section 4 shows that an analogy of Theorem 2 for dominant hyperbolic behavior (fractional Cattaneo–Vernotte equation) is not possible.

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Section: Uniqueness For Isp By Determination Of F(x) From the Final Time Observationmentioning

confidence: 99%

Some Inverse Source Problems of Determining a Space Dependent Source in Fractional-Dual-Phase-Lag Type Equations

Maes

Slodička

2020

Mathematics

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“…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. Direct and inverse problems for fractional partial differential equations have attracted much attention in various fields of the applied science; see previous studies 29–36 …”

Section: Introductionmentioning

confidence: 99%

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

Tekin

2021

Math Methods in App Sciences

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“…For a comprehensive tutorial on inverse problems for anomalous diffusion processes we refer to [22]. Identification of a space-dependent source factor h(x) in a source function of the form F(x, t) = h(x)q(x, t) from final overdetermination are studied in [17,19,[23][24][25], where different assumptions on the known source factor q(x, t) are discussed. Concerning the generalized subdiffusion equation, various types of inverse problems for such equations are studied in [26][27][28].…”

Section: Introductionmentioning

confidence: 99%

An Inverse Source Problem for the Generalized Subdiffusion Equation with Nonclassical Boundary Conditions

Bazhlekova

2021

Fractal Fract

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An initial-boundary-value problem is considered for the one-dimensional diffusion equation with a general convolutional derivative in time and nonclassical boundary conditions. We are concerned with the inverse source problem of recovery of a space-dependent source term from given final time data. Generalized eigenfunction expansions are used with respect to a biorthogonal pair of bases. Existence, uniqueness and stability estimates in Sobolev spaces are established.

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Uniqueness for an inverse source problem of determining a space dependent source in a time-fractional diffusion equation

Cited by 40 publications

References 16 publications

Some Inverse Source Problems of Determining a Space Dependent Source in Fractional-Dual-Phase-Lag Type Equations

Some Inverse Source Problems of Determining a Space Dependent Source in Fractional-Dual-Phase-Lag Type Equations

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

An Inverse Source Problem for the Generalized Subdiffusion Equation with Nonclassical Boundary Conditions

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