Acta mathematica scientia, Series B >
REGULARITY OF RANDOM ATTRACTORS FOR A STOCHASTIC DEGENERATE PARABOLIC EQUATIONS DRIVEN BY MULTIPLICATIVE NOISE
Received date: 2014-03-09
Revised date: 2014-08-07
Online published: 2016-04-25
Supported by
This work was supported by China NSF (11271388), Scientific and Technological Research Program of Chongqing Municipal Education Commission (KJ1400430), and Basis and Frontier Research Project of Chongqing (cstc2014jcyjA00035).
We study the regularity of random attractors for a class of degenerate parabolic equations with leading term div(σ(x)∇u) and multiplicative noises. Under some mild conditions on the diffusion variable σ(x) and without any restriction on the upper growth p of nonlinearity, except that p>2, we show the existences of random attractor in D01, 2(DN, σ)∩ L?(DN)(?∈[2, 2p-2]) space, where DN is an arbitrary (bounded or unbounded) domain in RN, N≥2. For this purpose, some abstract results based on the omega-limit compactness are established.
Wenqiang ZHAO . REGULARITY OF RANDOM ATTRACTORS FOR A STOCHASTIC DEGENERATE PARABOLIC EQUATIONS DRIVEN BY MULTIPLICATIVE NOISE[J]. Acta mathematica scientia, Series B, 2016 , 36(2) : 409 -427 . DOI: 10.1016/S0252-9602(16)30009-1
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