REGULARITY AND FRACTAL DIMENSION OF PULLBACK ATTRACTORS FOR A NON-AUTONOMOUS SEMILINEAR DEGENERATE PARABOLIC EQUATION

ANH, CUNG THE ; BAO, TANG QUOC ; THUY, LE THI

Glasgow mathematical journal, Tome 55 (2013) no. 2, pp. 431-448

Résumé

Considered here is the pullback attractor of the process associated with the first initial boundary value problem for the non-autonomous semilinear degenerate parabolic equation\begin{linenomath}u_t-\text{div}(\sigma(x)\nabla u)+f(u)=g(x,t)\end{linenomath}in a bounded domain Ω in RN (N≥2). We prove the regularity in the space L2p−2(Ω)∩ $D_0^2(\Omega,\sigma)$, and estimate the fractal dimension of the pullback attractor in L2(Ω).

Détail

DOI : 10.1017/S0017089512000663

Mots-clés : 37L30, 35B41, 35K65, 35D30

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