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Article

Global Nonexistence of Solutions of the Vibrations of a Riser

by
Vural Bayrak
* and
Mehmet Can
*
Istanbul Technical University Mathematics Department, Maslak. 80626 Istanbul Turkey
*
Authors to whom correspondence should be addressed.
Math. Comput. Appl. 1997, 2(1), 45-52; https://doi.org/10.3390/mca2010045
Published: 1 April 1997
Versions Notes

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.

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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. https://doi.org/10.3390/mca2010045

AMA Style

Bayrak V, Can M. Global Nonexistence of Solutions of the Vibrations of a Riser. Mathematical and Computational Applications. 1997; 2(1):45-52. https://doi.org/10.3390/mca2010045

Chicago/Turabian Style

Bayrak, Vural, and Mehmet Can. 1997. "Global Nonexistence of Solutions of the Vibrations of a Riser" Mathematical and Computational Applications 2, no. 1: 45-52. https://doi.org/10.3390/mca2010045

APA Style

Bayrak, V., & Can, M. (1997). Global Nonexistence of Solutions of the Vibrations of a Riser. Mathematical and Computational Applications, 2(1), 45-52. https://doi.org/10.3390/mca2010045

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