Bilgin, BA and Kalantarov, VK *About Blow up of Solutions With Arbitrary Positive Initial Energy to Nonlinear Wave Equations.* (Unpublished)

## Abstract

We show that blow up of solutions with arbitrary positive initial energy of the Cauchy problem for the abstract wacve eqation of the form $Pu_{tt}+Au=F(u) \ (*)$ in a Hilbert space, where $P,A$ are positive linear operators and $F(\cdot)$ is a continuously differentiable gradient operator can be obtained from the result of H.A. Levine on the growth of solutions of the Cauchy problem for (*). This result is applied to the study of inital boundary value problems for nonlinear Klein-Gordon equations, generalized Boussinesq equations and nonlinear plate equations. A result on blow up of solutions with positive initial energy of the initial boundary value problem for wave equation under nonlinear boundary condition is also obtained.

Item Type: | Article |
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Uncontrolled Keywords: | math.AP math.AP |

Subjects: | UNSPECIFIED |

Divisions: | Div B > Photonics |

Depositing User: | Cron Job |

Date Deposited: | 15 Aug 2017 01:22 |

Last Modified: | 11 Jan 2018 02:39 |

DOI: |