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1995 Self-similar solutions of a fast diffusion equation that do not conserve mass
M. A. Peletier, Hong Fei Zhang
Differential Integral Equations 8(8): 2045-2064 (1995).

Abstract

We consider self-similar solutions of the fast diffusion equation $u_t=\nabla\cdot(u^{-n}\nabla u)$ in $(0,\infty)\times\mathbb{R}^N$, for $N\geq3$ and $\frac2N<n<1$, of the form $ u(x,t) = (T-t)^\alpha f\left(\left|x\right|(T-t)^{-\beta}\right). $ Because mass conservation does not hold for these values of $n$, this results in a nonlinear eigenvalue problem for $f$, $\alpha$ and $\beta$. We employ phase plane techniques to prove existence and uniqueness of solutions $(f,\alpha,\beta)$, and we investigate their behaviour when $n\uparrow1$ and when $n\downarrow\frac2N$.

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M. A. Peletier. Hong Fei Zhang. "Self-similar solutions of a fast diffusion equation that do not conserve mass." Differential Integral Equations 8 (8) 2045 - 2064, 1995.

Information

Published: 1995
First available in Project Euclid: 20 May 2013

zbMATH: 0845.35057
MathSciNet: MR1348964

Subjects:
Primary: 35K55

Rights: Copyright © 1995 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.8 • No. 8 • 1995
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