BLOW-UP OF SMOOTH SOLUTIONS OF THE PROBLEM FOR A GENERALIZED DISPERSIVE EQUATION
Abstract
This work is devoted to studying the non-existence of the global-in-time solutions for the generalized Burger’s equation including Hilfer time fractional and Riemann-Liouville differential operators which in particular cases of the parameters follow the classical and other time-fractional Burgers equations. Applying the method of nonlinear capacity which S.I. Pokhozhaev suggested for some initial-boundary value problems, it has obtained sufficient conditions for the non-existence of global solutions
References
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 solution 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.
6.Pokhozhaev S.I. Essentially nonlinear capacities induced by differential operators. Dokl.Ros.Akad.Nauk. 357(5) (1997), 592-594.
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 solution 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.
6.Pokhozhaev S.I. Essentially nonlinear capacities induced by differential operators. Dokl.Ros.Akad.Nauk. 357(5) (1997), 592-594.
