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Some inverse source problems of determining a space dependent source in fractional-dual-phase-lag type equations

Frederick Maes (UGent) and Marian Slodicka (UGent)
(2020) MATHEMATICS. 8(8).
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Abstract
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 formh(t)f(x)with a known functionh(t). The unknown space dependent sourcef(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 onh(t)(monotonically increasing character ofh(t)was removed) in a case ofdominant parabolicbehavior. The proof technique was based on spectral analysis. Section Modified Model for tau q>tau Tshows that an analogy of Theorem 2 fordominant hyperbolicbehavior (fractional Cattaneo-Vernotte equation) is not possible.
Keywords
MAXIMUM PRINCIPLE, MODEL, LEQUATION, fractional dual-phase-lag equation, inverse source problem, uniqueness

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MLA
Maes, Frederick, and Marian Slodicka. “Some Inverse Source Problems of Determining a Space Dependent Source in Fractional-Dual-Phase-Lag Type Equations.” MATHEMATICS, vol. 8, no. 8, 2020, doi:10.3390/math8081291.
APA
Maes, F., & Slodicka, M. (2020). Some inverse source problems of determining a space dependent source in fractional-dual-phase-lag type equations. MATHEMATICS, 8(8). https://doi.org/10.3390/math8081291
Chicago author-date
Maes, Frederick, and Marian Slodicka. 2020. “Some Inverse Source Problems of Determining a Space Dependent Source in Fractional-Dual-Phase-Lag Type Equations.” MATHEMATICS 8 (8). https://doi.org/10.3390/math8081291.
Chicago author-date (all authors)
Maes, Frederick, and Marian Slodicka. 2020. “Some Inverse Source Problems of Determining a Space Dependent Source in Fractional-Dual-Phase-Lag Type Equations.” MATHEMATICS 8 (8). doi:10.3390/math8081291.
Vancouver
1.
Maes F, Slodicka M. Some inverse source problems of determining a space dependent source in fractional-dual-phase-lag type equations. MATHEMATICS. 2020;8(8).
IEEE
[1]
F. Maes and M. Slodicka, “Some inverse source problems of determining a space dependent source in fractional-dual-phase-lag type equations,” MATHEMATICS, vol. 8, no. 8, 2020.
@article{8700440,
  abstract     = {{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 formh(t)f(x)with a known functionh(t). The unknown space dependent sourcef(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 onh(t)(monotonically increasing character ofh(t)was removed) in a case ofdominant parabolicbehavior. The proof technique was based on spectral analysis. Section Modified Model for tau q>tau Tshows that an analogy of Theorem 2 fordominant hyperbolicbehavior (fractional Cattaneo-Vernotte equation) is not possible.}},
  articleno    = {{1291}},
  author       = {{Maes, Frederick and Slodicka, Marian}},
  issn         = {{2227-7390}},
  journal      = {{MATHEMATICS}},
  keywords     = {{MAXIMUM PRINCIPLE,MODEL,LEQUATION,fractional dual-phase-lag equation,inverse source problem,uniqueness}},
  language     = {{eng}},
  number       = {{8}},
  pages        = {{16}},
  title        = {{Some inverse source problems of determining a space dependent source in fractional-dual-phase-lag type equations}},
  url          = {{http://dx.doi.org/10.3390/math8081291}},
  volume       = {{8}},
  year         = {{2020}},
}

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