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Journals / Sigma Mühendislik ve Fen Bilimleri Dergisi / 2025 / Volume: 43 Issue: 1

Continuous dependence of solutions to a fourth order evolution equation

Sema Bayraktar(Department of Mathematics, Sakarya University, Sakarya, 54050, Türkiye)0000-0001-6063-0213
Emine Çelik(Department of Mathematics, Sakarya University, Sakarya, 54050, Türkiye)0000-0001-7567-0381
Şevket Gür(Department of Mathematics, Sakarya University, Sakarya, 54050, Türkiye)0000-0002-7180-5952
Pages
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Publication Date
2025-02-28
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AI Summary & Key Takeaways

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

Using energy estimates, we establish the continuous dependency for both the solution and its gradient concerning the fourth-order nonlinear parabolic equation.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We consider an initial-boundary value problem for a fourth-order nonlinear parabolic equation with constant coefficients.
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Key Findings & Data:Our primary focus lies in establishing a priori estimates for the solution to this equation, with a particular emphasis on its continuous dependence on both the initial data and parameters.
💡
Conclusion & Impact:Using energy estimates, we establish the continuous dependency for both the solution and its gradient concerning the fourth-order nonlinear parabolic equation.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Continuous Dependence · Energy Estimates · Fourth-Order Parabolic Equations

Abstract

We consider an initial-boundary value problem for a fourth-order nonlinear parabolic equation with constant coefficients. Our primary focus lies in establishing a priori estimates for the solution to this equation, with a particular emphasis on its continuous dependence on both the initial data and parameters. Using energy estimates, we establish the continuous dependency for both the solution and its gradient concerning the fourth-order nonlinear parabolic equation.

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Cite This Article

Bayraktar, S., Çelik, E., Gür, Ş. (2025). Continuous dependence of solutions to a fourth order evolution equation. Sigma Mühendislik ve Fen Bilimleri Dergisi, Volume: 43 Issue: 1. https://doi.org/10.14744/sigma.2025.00017

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