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A note on the quenching rate

Authors: Marek Fila and Josephus Hulshof
Journal: Proc. Amer. Math. Soc. 112 (1991), 473-477
MSC: Primary 35K60; Secondary 35B05
MathSciNet review: 1055772
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Abstract: We examine the quenching rate near a quenching point of a solution of a semilinear heat equation with singular powerlike absorption. A selfcontained result on similarity profiles allows us to improve a previous quenching theorem by Guo.

References [Enhancements On Off] (What's this?)

  • [FFM] A. Friedman, J. Friedman, and B. McLeod, Concavity of solutions of nonlinear ordinary differential equations, J. Math. Anal. Appl. 131 (1988), 486-500. MR 935283 (89c:34012)
  • [GK] Y. Giga and R. V. Kohn, Asymptotically self-similar blow-up for semilinear heat equations, Comm. Pure Appl. Math. 38 (1985), 297-319. MR 784476 (86k:35065)
  • [G1] J. Guo, On the quenching behavior of the solution of a semilinear parabolic equations, IMA preprint 447, 1988.
  • [G2] -, On the semilinear elliptic equation $ \Delta w - \frac{1}{2}y\nabla w + \lambda w - {w^{ - \beta }} = 0$ in $ {{\mathbf{R}}^n}$, unpublished.
  • [K] H. Kawarada, On solutions of initial boundary value problem for $ {u_t} = {u_{xx}} + \frac{1}{{1 - u}}$, Publ. Res. Inst. Math. Sci. 10 (1975), 729-736. MR 0385328 (52:6192)

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Keywords: Semilinear parabolic equation, quenching rate, similarity variables, second-order ordinary differential equation, convexity
Article copyright: © Copyright 1991 American Mathematical Society

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