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Journals / Mathematical and Computational Applications / 1997 / Cilt: 2 - Sayı: 1

Global nonexistence of solutions of the quasilinear hyperbolic equation of the vibrations of a riser

Vural BAYRAK
Mehmet CAN
Pages
45–52
DOI
—
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Hence one concludes that one cannot continue the solution for ail time by showing that this functional and hence the norm of the solution, would otherwise blow up in finite time.

📌 3 Key Takeaways

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Objective & Hypothesis:In this work, the nonexistence of the global solutions of a quasilinear hyperbolic boundary value problem with dissipative term in the equation is considered.
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Key Findings & Data:In one space dimension this initial value problem models the behavior of a riser vibrating due to the effects of waves and current.
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Conclusion & Impact:Hence one concludes that one cannot continue the solution for ail time by showing that this functional and hence the norm of the solution, would otherwise blow up in finite time.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

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 ail time by showing that this functional and hence the norm of the solution, would otherwise blow up in finite time.

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Cite This Article

BAYRAK, V., CAN, M. (1997). Global nonexistence of solutions of the quasilinear hyperbolic equation of the vibrations of a riser. Mathematical and Computational Applications, Cilt: 2 - Sayı: 1, 45–52. https://ajindex.com/articles/280212

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References (1)

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