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Journals / Turkish Journal of Mathematics and Computer Science / 2026 / Volume: 8

Quenching for A Nonlinear Diffusion Equation with Singular Boundary Outfluxes

Burhan Selçuk(KARABÜK ÜNİVERSİTESİ)
Nuri Özalp(ANKARA ÜNİVERSİTESİ)
Pages
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Publication Date
2018-06-30
DOI
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AI Summary & Key Takeaways

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

Finally, we show the time derivative blows up at the quenching time and we also establish results on quenching time and rate for certain nonlinearities.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper, we study a nonlinear diffusion equation (φ(u))_{t}=u_{xx}, 0<x<a, t>0 with singular boundary outfluxes u_{x}(0,t)=u^{-p}(0,t), u_{x}(a,t)=-u^{-q}(a,t).
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Key Findings & Data:Firstly, we get the quenchnig occurs in a finite time at the boundary x=a under certain conditions.
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Conclusion & Impact:Finally, we show the time derivative blows up at the quenching time and we also establish results on quenching time and rate for certain nonlinearities.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Heat equation · Nonlinear diffusion equation · nonlinear boundary condition

Abstract

In this paper, we study a nonlinear diffusion equation (φ(u))_{t}=u_{xx}, 0<x<a, t>0 with singular boundary outfluxes u_{x}(0,t)=u^{-p}(0,t), u_{x}(a,t)=-u^{-q}(a,t). Firstly, we get the quenchnig occurs in a finite time at the boundary x=a under certain conditions. Finally, we show the time derivative blows up at the quenching time and we also establish results on quenching time and rate for certain nonlinearities.

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Cite This Article

Selçuk, B., Özalp, N. (2018). Quenching for A Nonlinear Diffusion Equation with Singular Boundary Outfluxes. Turkish Journal of Mathematics and Computer Science, Volume: 8. https://ajindex.com/articles/1324953

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References (9)

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