Research Article
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Year 2023, Volume: 72 Issue: 2, 500 - 511, 23.06.2023
https://doi.org/10.31801/cfsuasmas.1127250

Abstract

References

  • Arancibia, R., Lecaros, R., Mercado, A., Zamorano, S., An inverse problem for Moore-Gibson-Thompson equation arising in high intensity ultrasound, Journal of Inverse and Ill-posed Problems, 30(5) 82022, 659-675. https://doi.org/10.1515/jiip-2020-0090
  • Chlouverakis, K. E., Sprott, J. C., Chaotic hyperjerk systems, Chaos, Solitons & Fractals, 28(3) (2006), 739-746. https://doi.org/10.1016/j.chaos.2005.08.019
  • Choucha, A., Boulaaras, S., Ouchenane, D., Abdalla, M., Mekawy, I., Benbella, A., Existence and uniqueness for Moore-Gibson-Thompson equation with, source terms, viscoelastic memory and integral condition, AIMS Mathematics, 6(7) (2021), 7585-7624.
  • Conti, M., Pata, V., Quintanilla, R., Thermoelasticity of Moore-Gibson-Thompson type with history dependence in the temperature, Asymptotic Analysis, 120(1-2) (2020), 1-21. https://doi.org/10.3233/ASY-191576
  • Dell’Oro, F., Pata, V., On a fourth-order equation of Moore-Gibson-Thompson type, Milan J. Math., 85 (2017), 215-234.
  • Dell’Oro, F., Pata, V., On the Moore-Gibson-Thompson equation and its relation to linear viscoelasticity, Applied Mathematics & Optimization, 7683 (2017), 641-655. https://doi.org/10.1007/s00245-016-9365-1
  • Dell’ Oro, F., Lasiecka, I., Pata, V., The Moore-Gibson-Thompson equation with memory in the critical case, J Differ Equ., 261 (2016), 4188-4222. https://doi.org/10.1016/j.jde.2016.06.025
  • Figliolini, G., Lanni, C., Jerk and jounce relevance for the kinematic performance of long-dwell mechanisms, Mechanisms and Machine Science, 73 (2019), 219-228. https://doi.org/10.1007/978-3-030-20131-9 22
  • Huntul, M. J., Tekin, I., On an inverse problem for a nonlinear third order in time partial differential equation, Results in Applied Mathematics, 15 (2022), 100314. https://doi.org/10.1016/j.rinam.2022.100314
  • Kaltenbacher, B., Lasiecka, I., Pospieszalska, M. K., Well-posedness and exponential decay of the energy in the nonlinear Jordan-Moore-Gibson-Thompson equation arising in high intensity ultrasound, Mathematical Models and Methods in Applied Sciences, 22(11) (2012), 1250035. https://doi.org/10.1142/S0218202512500352
  • Kaltenbacher, B., Nikolic, V., The Jordan-Moore-Gibson-Thompson equation: wellposedness with quadratic gradient nonlinearity and singular limit for vanishing relaxation time, Mathematical Models and Methods in Applied Sciences, 29(13) (2019), 2523-2556. https://doi.org/10.1142/S0218202519500532
  • Kaltenbacher, B., Mathematics of nonlinear acoustics, Evolution Equations & Control Theory, 4(4) (2015), 447-491.
  • Lasiecka, I., Wang, X., Moore-Gibson-Thompson equation with memory, part I: exponential decay of energy, Zeitschrift f¨ur angewandte Mathematik und Physik, 67(2) (2016), 1-23. https://doi.org/10.1007/s00033-015-0597-8
  • Lasiecka, I., Wang, X., Moore-Gibson-Thompson equation with memory, part II: general decay of energy, Journal of Differential Equations, 259(12) (2015), 7610-7635. https://doi.org/10.1016/j.jde.2015.08.052
  • Liu, W., Chen, Z., Tu, Z., New general decay result for a fourth-order Moore-Gibson-Thompson equation with memory, Electronic Research Archive, 28(1) (2020), 433. https://doi.org/10.3934/era.2020025
  • Lizama, C., Murillo-Arcila, M., well-posedness for a fourth-order equation of Moore-Gibson-Thompson type, Electronic Journal of Qualitative Theory of Differential Equations, 81 (2021), 1-18. https://doi.org/10.14232/ejqtde.2021.1.81
  • Mehraliyev, Y. T., On solvability of an inverse boundary value problem for a second order elliptic equation, Bulletin of Tver State University, Series: Applied mathematics, 23 (2011), 25-38. (in Russian)
  • Mesloub, A., Zara, A., Mesloub, F., Cherif, B. B., Abdalla, M., The Galerkin method for fourth-Order equation of the Moore-Gibson-Thompson type with integral condition, Advances in Mathematical Physics, (2021), 2021. https://doi.org/10.1155/2021/5532691
  • Murillo-Arcila, M., Well-posedness for the fourth-order Moore-Gibson-Thompson equation in the class of Banach-space-valued H¨older-continuous functions, Mathematical Methods in the Applied Sciences, (2022), 1-10. doi:10.1002/mma.8618
  • Pellicer Sabadi, M., Said-Houari,B., Well posedness and decay rates for the Cauchy problem of the Moore-Gibson-Thompson equation arising in high intensity ultrasound, Applied Mathematics and Optimization, 80(2) 82019), 447-478. https://doi.org/10.1007/s00245-017-9471-8
  • Tekin, I., Inverse problem for a nonlinear third order in time partial differential equation, Mathematical Methods in the Applied Sciences, 44(11) (2021), 9571-9581. https://doi.org/10.1002/mma.7380
  • Visser, M., Jerk, snap and the cosmological equation of state, Classical and Quantum Gravity, 21(11) (2004), 2603. https://doi.org/10.1088/0264-9381/21/11/006

Identification of the time-dependent lowest term in a fourth order in time partial differential equation

Year 2023, Volume: 72 Issue: 2, 500 - 511, 23.06.2023
https://doi.org/10.31801/cfsuasmas.1127250

Abstract

In this article, identification of the time-dependent lowest term in a fourth order in time partial differential equation (PDE) from knowledge of a boundary measurement is studied by means of contraction mapping.

References

  • Arancibia, R., Lecaros, R., Mercado, A., Zamorano, S., An inverse problem for Moore-Gibson-Thompson equation arising in high intensity ultrasound, Journal of Inverse and Ill-posed Problems, 30(5) 82022, 659-675. https://doi.org/10.1515/jiip-2020-0090
  • Chlouverakis, K. E., Sprott, J. C., Chaotic hyperjerk systems, Chaos, Solitons & Fractals, 28(3) (2006), 739-746. https://doi.org/10.1016/j.chaos.2005.08.019
  • Choucha, A., Boulaaras, S., Ouchenane, D., Abdalla, M., Mekawy, I., Benbella, A., Existence and uniqueness for Moore-Gibson-Thompson equation with, source terms, viscoelastic memory and integral condition, AIMS Mathematics, 6(7) (2021), 7585-7624.
  • Conti, M., Pata, V., Quintanilla, R., Thermoelasticity of Moore-Gibson-Thompson type with history dependence in the temperature, Asymptotic Analysis, 120(1-2) (2020), 1-21. https://doi.org/10.3233/ASY-191576
  • Dell’Oro, F., Pata, V., On a fourth-order equation of Moore-Gibson-Thompson type, Milan J. Math., 85 (2017), 215-234.
  • Dell’Oro, F., Pata, V., On the Moore-Gibson-Thompson equation and its relation to linear viscoelasticity, Applied Mathematics & Optimization, 7683 (2017), 641-655. https://doi.org/10.1007/s00245-016-9365-1
  • Dell’ Oro, F., Lasiecka, I., Pata, V., The Moore-Gibson-Thompson equation with memory in the critical case, J Differ Equ., 261 (2016), 4188-4222. https://doi.org/10.1016/j.jde.2016.06.025
  • Figliolini, G., Lanni, C., Jerk and jounce relevance for the kinematic performance of long-dwell mechanisms, Mechanisms and Machine Science, 73 (2019), 219-228. https://doi.org/10.1007/978-3-030-20131-9 22
  • Huntul, M. J., Tekin, I., On an inverse problem for a nonlinear third order in time partial differential equation, Results in Applied Mathematics, 15 (2022), 100314. https://doi.org/10.1016/j.rinam.2022.100314
  • Kaltenbacher, B., Lasiecka, I., Pospieszalska, M. K., Well-posedness and exponential decay of the energy in the nonlinear Jordan-Moore-Gibson-Thompson equation arising in high intensity ultrasound, Mathematical Models and Methods in Applied Sciences, 22(11) (2012), 1250035. https://doi.org/10.1142/S0218202512500352
  • Kaltenbacher, B., Nikolic, V., The Jordan-Moore-Gibson-Thompson equation: wellposedness with quadratic gradient nonlinearity and singular limit for vanishing relaxation time, Mathematical Models and Methods in Applied Sciences, 29(13) (2019), 2523-2556. https://doi.org/10.1142/S0218202519500532
  • Kaltenbacher, B., Mathematics of nonlinear acoustics, Evolution Equations & Control Theory, 4(4) (2015), 447-491.
  • Lasiecka, I., Wang, X., Moore-Gibson-Thompson equation with memory, part I: exponential decay of energy, Zeitschrift f¨ur angewandte Mathematik und Physik, 67(2) (2016), 1-23. https://doi.org/10.1007/s00033-015-0597-8
  • Lasiecka, I., Wang, X., Moore-Gibson-Thompson equation with memory, part II: general decay of energy, Journal of Differential Equations, 259(12) (2015), 7610-7635. https://doi.org/10.1016/j.jde.2015.08.052
  • Liu, W., Chen, Z., Tu, Z., New general decay result for a fourth-order Moore-Gibson-Thompson equation with memory, Electronic Research Archive, 28(1) (2020), 433. https://doi.org/10.3934/era.2020025
  • Lizama, C., Murillo-Arcila, M., well-posedness for a fourth-order equation of Moore-Gibson-Thompson type, Electronic Journal of Qualitative Theory of Differential Equations, 81 (2021), 1-18. https://doi.org/10.14232/ejqtde.2021.1.81
  • Mehraliyev, Y. T., On solvability of an inverse boundary value problem for a second order elliptic equation, Bulletin of Tver State University, Series: Applied mathematics, 23 (2011), 25-38. (in Russian)
  • Mesloub, A., Zara, A., Mesloub, F., Cherif, B. B., Abdalla, M., The Galerkin method for fourth-Order equation of the Moore-Gibson-Thompson type with integral condition, Advances in Mathematical Physics, (2021), 2021. https://doi.org/10.1155/2021/5532691
  • Murillo-Arcila, M., Well-posedness for the fourth-order Moore-Gibson-Thompson equation in the class of Banach-space-valued H¨older-continuous functions, Mathematical Methods in the Applied Sciences, (2022), 1-10. doi:10.1002/mma.8618
  • Pellicer Sabadi, M., Said-Houari,B., Well posedness and decay rates for the Cauchy problem of the Moore-Gibson-Thompson equation arising in high intensity ultrasound, Applied Mathematics and Optimization, 80(2) 82019), 447-478. https://doi.org/10.1007/s00245-017-9471-8
  • Tekin, I., Inverse problem for a nonlinear third order in time partial differential equation, Mathematical Methods in the Applied Sciences, 44(11) (2021), 9571-9581. https://doi.org/10.1002/mma.7380
  • Visser, M., Jerk, snap and the cosmological equation of state, Classical and Quantum Gravity, 21(11) (2004), 2603. https://doi.org/10.1088/0264-9381/21/11/006
There are 22 citations in total.

Details

Primary Language English
Subjects Partial Differential Equations, Applied Mathematics
Journal Section Research Articles
Authors

İbrahim Tekin 0000-0001-6725-5663

Publication Date June 23, 2023
Submission Date June 7, 2022
Acceptance Date October 31, 2022
Published in Issue Year 2023 Volume: 72 Issue: 2

Cite

APA Tekin, İ. (2023). Identification of the time-dependent lowest term in a fourth order in time partial differential equation. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 72(2), 500-511. https://doi.org/10.31801/cfsuasmas.1127250
AMA Tekin İ. Identification of the time-dependent lowest term in a fourth order in time partial differential equation. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2023;72(2):500-511. doi:10.31801/cfsuasmas.1127250
Chicago Tekin, İbrahim. “Identification of the Time-Dependent Lowest Term in a Fourth Order in Time Partial Differential Equation”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72, no. 2 (June 2023): 500-511. https://doi.org/10.31801/cfsuasmas.1127250.
EndNote Tekin İ (June 1, 2023) Identification of the time-dependent lowest term in a fourth order in time partial differential equation. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72 2 500–511.
IEEE İ. Tekin, “Identification of the time-dependent lowest term in a fourth order in time partial differential equation”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 72, no. 2, pp. 500–511, 2023, doi: 10.31801/cfsuasmas.1127250.
ISNAD Tekin, İbrahim. “Identification of the Time-Dependent Lowest Term in a Fourth Order in Time Partial Differential Equation”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72/2 (June 2023), 500-511. https://doi.org/10.31801/cfsuasmas.1127250.
JAMA Tekin İ. Identification of the time-dependent lowest term in a fourth order in time partial differential equation. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72:500–511.
MLA Tekin, İbrahim. “Identification of the Time-Dependent Lowest Term in a Fourth Order in Time Partial Differential Equation”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 72, no. 2, 2023, pp. 500-11, doi:10.31801/cfsuasmas.1127250.
Vancouver Tekin İ. Identification of the time-dependent lowest term in a fourth order in time partial differential equation. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72(2):500-11.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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