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Optimal estimates for blowup rate and behavior for nonlinear heat equations

✍ Scribed by Frank Merle; Hatem Zaag

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
498 KB
Volume
51
Category
Article
ISSN
0010-3640

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✦ Synopsis

We first describe all positive bounded solutions of

and (N -2)p ≀ N + 2. We then obtain for blowup solutions u(t) of βˆ‚u βˆ‚t = βˆ†u + u p uniform estimates at the blowup time and uniform space-time comparison with solutions of u = u p .

πŸ“œ SIMILAR VOLUMES

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We prove a Liouville theorem for the following heat system whose nonlinearity has no gradient structure: where pq > 1, p β‰₯ 1, q β‰₯ 1, and | p -q| small. We then deduce a localization property and uniform L ∞ estimates of blowup solutions of this system.

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