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Math. Comput. Appl. 1997, 2(1), 45-52; doi:10.3390/mca2010045

Global Nonexistence of Solutions of the Vibrations of a Riser

Istanbul Technical University Mathematics Department, Maslak. 80626 Istanbul Turkey
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Published: 1 April 1997
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Abstract

In this work, the nonexistence of the global solutions of a quasilinear hyperbolic boundary value problem with dissipative term in the equation is considered. In one space dimension this initial value problem models the behavior of a riser vibrating due to the effects of waves and current. The nonexistence proof is achieved by the use of the so called concavity method. In this method one writes down a functional which represents the norm of the solution in some sense. Then it is proved that this functional satisfies the hypotheses of the concavity lemma. Hence one concludes that one cannot continue the solution for all time by showing that this functional and hence the norm of the solution, would otherwise blow up in finite time.
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Bayrak, V.; Can, M. Global Nonexistence of Solutions of the Vibrations of a Riser. Math. Comput. Appl. 1997, 2, 45-52.

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