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

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.

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