✦ LIBER ✦

Blow-up of solutions to parabolic equations with nonstandard growth conditions

✍ Scribed by S. Antontsev; S. Shmarev

Publisher: Elsevier Science
Year: 2010
Tongue: English
Weight: 410 KB
Volume: 234
Category: Article
ISSN: 0377-0427
DOI: 10.1016/j.cam.2010.01.026

No coin nor oath required. For personal study only.

✦ Synopsis

We study the phenomenon of finite time blow-up in solutions of the homogeneous Dirichlet problem for the parabolic equation

we show that the finite time blow-up happens if the initial function is sufficiently large and either min

In the case of the evolution p(x)-Laplace equation with the exponents p(x), σ (x) independent of t, we prove that every solution corresponding to a sufficiently large initial function exhibits a finite time blow-up if b(x, t) ≥ b -> 0, a t (x, t) ≤ 0, b t (x, t) ≥ 0, min σ (x) > 2 and max p(x) ≤ min σ (x).

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