BLOW-UP OF SMOOTH SOLUTIONS OF THE PROBLEM FOR THE KORTEWEG-DE VRIES-BURGERS EQUATION WITH THE HILFER FRACTIONAL DIFFERENTIAL OPERATOR

Авторлор

  • Азизбек Маманазаров Fergana State University
  • Диёрбек Мухторов Fergana State University

DOI:

https://doi.org/10.52754/16948645_2024_1(4)_47

Ачкыч сөздөр:

Hilfer derivative, the method of nonlinear capacity, non-existence of the solution

Аннотация

This work is devoted to studying the non-existence of the global-in-time solutions for the Korteweg-de Vries-Burgers equation including Hilfer time fractional differential operator which in particular cases of the parameters follows the classical and other time-fractional Korteweg-de Vries-Burgers equation. Applying the method of nonlinear capacity which was suggested by S.I. Pokhozhaev for some initial-boundary value problems, it has been obtained sufficient conditions for the non-existence of global solutions.

Библиографиялык шилтемелер

Kilbas A.A., Srivastava H.M. and Trujillo J.J. Theory and Applications of Fractional Differential Equations, Elsevier, North-Holland, 2006.

Hilfer R. Applications of Fractional Calculus in Physics. World Scientific, Singapore, 200, p.87 and p.429.

Hilfer R. Experimental evidence for fractional time evolution in glass materials, Chem. Physics. 284 (2002), 399-408. DOI: https://doi.org/10.1016/S0301-0104(02)00670-5

Ahmed Alsaedi, Mokhtar Kirane and Berikbol T.Torebek (2020) Blow-up smooth solutions of the time-fractional Burger equation, Questiones Mathematical, 43:2, 185-192, DOI:10.2989/16073606.2018.1544596. DOI: https://doi.org/10.2989/16073606.2018.1544596

Burger J.M. A Mathematical Model Illustrating the Theory of Turbulence, Adv.in Appl. Mech. I, pp.171-199, Academic Pres, New York, 1948. DOI: https://doi.org/10.1016/S0065-2156(08)70100-5

Pokhozhaev S.I. Essentially nonlinear capacities induced by differential operators. Dokl.Ros. Akad. Nauk. 357(5) (1997), 592-594.

Жүктөөлөр

Жарыяланды

2024-06-11

Кандай шилтеме берүү керек

Маманазаров, А., & Мухторов , Д. (2024). BLOW-UP OF SMOOTH SOLUTIONS OF THE PROBLEM FOR THE KORTEWEG-DE VRIES-BURGERS EQUATION WITH THE HILFER FRACTIONAL DIFFERENTIAL OPERATOR. Ош мамлекеттик университетинин Жарчысы. Математика. Физика. Техника, (1(4), 251–255. https://doi.org/10.52754/16948645_2024_1(4)_47

Саны (чыгарылыш)

№ 1(4) (2024): ОШ МАМЛЕКЕТТИК УНИВЕРСИТЕТИНИН ЖАРЧЫСЫ МАТЕМАТИКА. ФИЗИКА. ТЕХНИКА

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МАТЕМАТИКА

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