BLOW-UP OF SMOOTH SOLUTIONS OF THE PROBLEM FOR THE KORTEWEG-DE VRIES-BURGERS EQUATION WITH THE HILFER FRACTIONAL DIFFERENTIAL OPERATOR
DOI:
https://doi.org/10.52754/16948645_2024_1(4)_47Keywords:
Hilfer derivative, the method of nonlinear capacity, non-existence of the solutionAbstract
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.
References
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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
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Pokhozhaev S.I. Essentially nonlinear capacities induced by differential operators. Dokl.Ros. Akad. Nauk. 357(5) (1997), 592-594.
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