Quenching for a nonlinear diffusion equation with a singular boundary condition

  • K. Deng
  • M. Xu

DOI: 10.1007/s000330050167

Cite this article as:
Deng, K. & Xu, M. Z. angew. Math. Phys. (1999) 50: 574. doi:10.1007/s000330050167

Abstract.

We study a nonlinear diffusion equation \((\psi (u))_t =u_{xx},\0 < x < 1,\t > 0\) with a singular boundary condition \(u_x(1,t) = -g(u(1,t))\). We prove finite time quenching for the solution. We also establish results on quenching set and rate.

Key words. Nonlinear diffusion equation, singular boundary condition, finite time quenching, quenching set, quenching rate. 

Copyright information

© Birkhäuser Verlag, Basel, 1999

Authors and Affiliations

  • K. Deng
    • 1
  • M. Xu
    • 1
  1. 1.Department of Mathematics, University of Southwestern Louisiana, Lafayette, LA 70504, USA, e-mail:kxd5858@usl.eduUS

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