Author:
Mamanazarov Azizbek,Mukhtorov Diyorbek
Abstract
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.
Reference6 articles.
1. Kilbas A.A., Srivastava H.M. and Trujillo J.J. Theory and Applications of Fractional Differential Equations, Elsevier, North-Holland, 2006.
2. Hilfer R. Applications of Fractional Calculus in Physics. World Scientific, Singapore, 200, p.87 and p.429.
3. Hilfer R. Experimental evidence for fractional time evolution in glass materials, Chem. Physics. 284 (2002), 399-408.
4. 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.
5. Burger J.M. A Mathematical Model Illustrating the Theory of Turbulence, Adv.in Appl. Mech. I, pp.171-199, Academic Pres, New York, 1948.