### Electronic Research Archive

2020, Issue 1: 347-367. doi: 10.3934/era.2020020
Special Issues

# Blow-up in damped abstract nonlinear equations

• 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.

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

### Related Papers:

• 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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