REGULARITY AND FRACTAL DIMENSION OF PULLBACK ATTRACTORS FOR A NON-AUTONOMOUS SEMILINEAR DEGENERATE PARABOLIC EQUATION
2013; Cambridge University Press; Volume: 55; Issue: 2 Linguagem: Inglês
10.1017/s0017089512000663
ISSN1469-509X
AutoresCung The Anh, Bao Quoc Tang, Lê Thị Thủy,
Tópico(s)Nonlinear Partial Differential Equations
ResumoAbstract 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 ℝ N (N≥2). We prove the regularity in the space L 2 p −2 (Ω)∩ $D_0^2(\Omega,\sigma)$ , and estimate the fractal dimension of the pullback attractor in L 2 (Ω).
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