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Journals / Turkish Journal of Mathematics and Computer Science / 2018 / Cilt: 8 - Sayı: 8

Quenching for A Nonlinear Diffusion Equation with Singular Boundary Outfluxes

Burhan Selcuk
Nuri Ozalp
Pages
65–69
Publication Date
2022-11-03
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 timeand we also establish results on quenching time and rate for certain nonlinearities.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we study a nonlinear diffusion equation (φ(u))t = uxx, 0 0 with singularboundary outfluxes ux(0, t) = u−p(0, t), ux(a, t) = −u−q(a, t).
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Key Findings & Data:Firstly, we get the quenching occurs in a finite time atthe boundary x = a under certain conditions.
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Conclusion & Impact:Finally, we show the time derivative blows up at the quenching timeand we also establish results on quenching time and rate for certain nonlinearities.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, we study a nonlinear diffusion equation (φ(u))t = uxx, 0 0 with singularboundary outfluxes ux(0, t) = u−p(0, t), ux(a, t) = −u−q(a, t). Firstly, we get the quenching occurs in a finite time atthe boundary x = a under certain conditions. Finally, we show the time derivative blows up at the quenching timeand we also establish results on quenching time and rate for certain nonlinearities.

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Cite This Article

Selcuk, B., Ozalp, N. (2022). Quenching for A Nonlinear Diffusion Equation with Singular Boundary Outfluxes. Turkish Journal of Mathematics and Computer Science, Cilt: 8 - Sayı: 8, 65–69. https://ajindex.com/articles/609173

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References (9)

  1. Deng, K., Xu, M., Quenching for a nonlinear diffusion equation with a singular boundary condition, Z. Angew. Math. Phys., 50(1999), 574–584
  2. Fila, M., Levine, H.A., Quenching on the boundary, Nonlinear Anal., 21(1993), 795–802
  3. Pao, C.V., Quasilinear parabolic and elliptic equations with nonlinear boundary conditions, Nonlinear Analysis, 66(2007), 639–662
  4. Selcuk, B., Ozalp, N., Quenching behavior of semilinear heat equations with singular boundary conditions, Electron. J. Diff. Equ., 2015(311)(2015), 1–13
  5. Selcuk, B., Ozalp, N., Quenching for a semilinear heat equation with a singular boundary outflux, Int. J. Appl. Math, 29(4)(2016), 451–464
  6. Yang, Y., Quenching phenomenon for a non-Newtonian filtration equation with singular boundary flux, Boundary Value Problems, (2015), 2015:233
  7. Yang, Y., Yin, J., Jin, C., Quenching phenomenon of positive radial solutions for p-Laplacian with singular boundary flux, J. Dyn.Control Syst., 22(2016), 653–660
  8. Yang, Y., Finite time quenching for a nonlinear diffusion equation with singular boundary flux, Journal of Physics: Conference Series, 814(1)(2017), 1–6
  9. Zhi, Y., Mu, C., The quenching behavior of a nonlinear parabolic equation with a nonlinear boundary outflux, Appl. Math.Comput., 184(2007), 624–630.