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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Under the condition of positive initial energy we show that the solution for this problem blows up in finite time.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper we consider a mixed problem for the nonlinear wave equations with transmission acoustic conditions, that is, the wave propagation over bodies consisting of two physically different types of materials, one of which is clamped.
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Key Findings & Data:We prove the existence of a global solution.
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Conclusion & Impact:Under the condition of positive initial energy we show that the solution for this problem blows up in finite time.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Nonlinear wave equation · transmission acoustic conditions · locally reacting boundary
Abstract
In this paper we consider a mixed problem for the nonlinear wave equations with transmission acoustic conditions, that is, the wave propagation over bodies consisting of two physically different types of materials, one of which is clamped. We prove the existence of a global solution. Under the condition of positive initial energy we show that the solution for this problem blows up in finite time.
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Cite This Article
ALIYEV, A., ISAYEVA, S. (2018). Existence and nonexistence of global solutions for nonlinear transmission acoustic problem. Turkish Journal of Mathematics, Cilt: 42 - Sayı: 6, 3211–3231. https://ajindex.com/articles/227832