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Blow-up and propagation of disturbances for fast diffusion equations

✍ Scribed by Paul-Emile Maingé

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
313 KB
Volume
68
Category
Article
ISSN
0362-546X

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✦ Synopsis

This paper is concerned with the Cauchy problem for the fast diffusion equation u t -∆u m = αu p 1 in R N (N ≥ 1), where m ∈ (0, 1), p 1 > 1 and α > 0. The initial condition u 0 is assumed to be continuous, nonnegative and bounded. Using a technique of subsolutions, we set up sufficient conditions on the initial value u 0 so that u(t, x) blows up in finite time, and we show how to get estimates on the profile of u(t, x) for small enough values of t > 0.

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