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Decay of Mass for the Equation ut=Δu−a(x) up |∇u|q

✍ Scribed by Ross G Pinsky

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 189 KB
Volume: 165
Category: Article
ISSN: 0022-0396
DOI: 10.1006/jdeq.2000.3771

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✦ Synopsis

Consider the quasilinear Cauchy problem

where a>0, p and q satisfy p 0 and q 1 or p>1 and q=0, and

This paper proves that the above equation possesses a unique positive classical solution and then investigates whether or not ##lim t Ä R d u(x, t) dx=0. In particular, it is shown that if a is on the order |x| m for large |x|, then #=0 if dp+(d+1) q d+2+m. Under the assumption that for compactly supported ,,

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Decay of Mass for the Equation ut=Δu−a(x)&#xa0;up&#xa0;|∇u|q

✦ Synopsis

Decay of Mass for the Equation ut=Δu−a(x) up |∇u|q