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Journals / Contemporary Analysis and Applied Mathematics / 2013 / Cilt: 1 - Sayı: 1

Çift dispersif altıncı mertebeden Boussinesq denklemi için global varlık

Global existence for a double dispersive sixth order Boussinesq equation

Hatice TASKESEN
Necat POLAT
Pages
60–69
Publication Date
2022-10-11
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

A new functional, which includes not only initial displacement but also initial velocity, will be defined for the potential well method, and by the aid of sign invariance of this functional the Cauchy problem for the supercritical initial energy will be considered.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, existence of global weak solutions for the double dispersive sixth order Boussinesq equation with power type nonlinearity β |u| p and supercritical initial energy will be investigated.
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Key Findings & Data:In this paper, existence of global weak solutions for the double dispersive sixth order Boussinesq equation with power type nonlinearity β |u| p and supercritical initial energy will be investigated.
💡
Conclusion & Impact:A new functional, which includes not only initial displacement but also initial velocity, will be defined for the potential well method, and by the aid of sign invariance of this functional the Cauchy problem for the supercritical initial energy will be considered.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, existence of global weak solutions for the double dispersive sixth order Boussinesq equation with power type nonlinearity β |u| p and supercritical initial energy will be investigated. A new functional, which includes not only initial displacement but also initial velocity, will be defined for the potential well method, and by the aid of sign invariance of this functional the Cauchy problem for the supercritical initial energy will be considered.

Özet

Bu makalede altıncı mertebeden çift dispersif terimli Boussinesq denkleminin β |u| p tipli doğrusal olmayan terimi ve süperkritik başlangıç enerjisiyle global zayıf çözümlerinin varlığı incelenmiştir. Potential well metodu için hem başlangıç yer değişimini hem de başlangıç hızını içeren bir fonksiyonel tanımlanmış ve Cauchy problemi süperkritik başlangıç enerjisi için bu fonksiyonelin işaret değişmezliği yardı- mıyla ele alınmıştır.

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Cite This Article

TASKESEN, H., POLAT, N. (2022). Çift dispersif altıncı mertebeden Boussinesq denklemi için global varlık. Contemporary Analysis and Applied Mathematics, Cilt: 1 - Sayı: 1, 60–69. https://ajindex.com/articles/476494

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References (1)

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