## Abstract

We consider the fractional in time acoustic wave equation (Formula presented.) where 1<α<2, (Formula presented.) is the Caputo fractional derivative of order α, u=u(t,x), t>0, (Formula presented.), is the pressure in the medium, ε is the nonlinear acoustic parameter, ρ_{0} is the equilibrium density in the medium, and c_{0} is the equilibrium sound velocity. We study a Cauchy problem for this equation and a mixed boundary value problem in a bounded domain. For each problem, sufficient conditions for the blow-up of solutions are derived. Moreover, we provide a class of initial data for which there are no classical solutions even locally in time. Our approach is based on the nonlinear capacity method.

Original language | British English |
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Pages (from-to) | 6566-6575 |

Number of pages | 10 |

Journal | Mathematical Methods in the Applied Sciences |

Volume | 43 |

Issue number | 10 |

DOIs | |

State | Published - 15 Jul 2020 |

## Keywords

- blow-up
- Caputo fractional derivative
- fractional in time acoustic wave equation