Blow-up in damped abstract nonlinear equations

Jorge A. Esquivel-Avila; Jorge A. Esquivel-Avila

doi:10.3934/era.2020020

Electronic Research Archive

2020, Volume 28, Issue 1: 347-367. doi: 10.3934/era.2020020

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Blow-up in damped abstract nonlinear equations

Jorge A. Esquivel-Avila ^{1
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Universidad Autónoma Metropolitana, Unidad Azcapotzalco, Av. San Pablo 180, Col. Reynosa Tamaulipas, 02200 Azcapotzalco, CDMX, México

Received: 01 December 2019 Revised: 01 February 2020
Primary: 35L70, 35L90, 35B44, 35L05; Secondary: 35B35, 35B40

As a typical example of our analysis we consider a generalized Boussinesq equation, linearly damped and with a nonlinear source term. For any positive value of the initial energy, in particular for high energies, we give sufficient conditions on the initial data to conclude nonexistence of global solutions. We do our analysis in an abstract framework. We compare our results with those in the literature and we give more examples to illustrate the applicability of the abstract formulation.
- Hyperbolic equations,
- generalized Boussinesq equation,
- blow-up,
- high energies
Citation: Jorge A. Esquivel-Avila. Blow-up in damped abstract nonlinear equations[J]. Electronic Research Archive, 2020, 28(1): 347-367. doi: 10.3934/era.2020020

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Abstract

As a typical example of our analysis we consider a generalized Boussinesq equation, linearly damped and with a nonlinear source term. For any positive value of the initial energy, in particular for high energies, we give sufficient conditions on the initial data to conclude nonexistence of global solutions. We do our analysis in an abstract framework. We compare our results with those in the literature and we give more examples to illustrate the applicability of the abstract formulation.

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