Burhan Selcuk, Nuri Ozalp

Quenching for A Nonlinear Diffusion Equation with Singular Boundary Outfluxes

ISSN: 2148-1830
Yayın Aralığı: 2
Başlangıç: 2013
Yayıncı: MATEMATİKÇİLER DERNEĞİ

In this paper, we study a nonlinear diffusion equation (φ(u))t = uxx, 0 < x < a, t > 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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[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.