Blow up and boundedness for high energies of a quasilinear riser equation
β Scribed by Jorge A. Esquivel-Avila
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 515 KB
- Volume
- 71
- Category
- Article
- ISSN
- 0362-546X
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β¦ Synopsis
We consider a quasilinear wave equation of fourth order that models the mechanical vibrations of a marine riser. We study qualitative properties such as boundedness and blow up of solutions with respect to the norm of some Hilbert space H, for any real value of the initial energy. To this end we use invariant sets.
π SIMILAR VOLUMES
In this paper, we consider the following Kirchhoff type equation: with initial condition and zero Dirichlet boundary condition. We established sufficient conditions on the initial data with arbitrarily high energy such that the solution blows up in finite time. This result generalizes and improves
## For suitable and F, we prove that all classical solutions of the quasilinear wave equation RR !( ( V )) V "F(), with initial data of compact support, develop singularities in "nite time. The assumptions on and F include in particular the model case O>, for q\*2, and "$1. The starting point of