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

Published online by Cambridge University Press:  25 February 2013

CUNG THE ANH ,
TANG QUOC BAO  and
LE THI THUY
CUNG THE ANH
Affiliation:
Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam e-mail: anhctmath@hnue.edu.vn
TANG QUOC BAO
Affiliation:
Faculty of Applied Mathematics and Informatics, Hanoi University of Science and Technology, 1 Dai Co Viet, Hai Ba Trung, Hanoi, Vietnam e-mail: mathizonewww@gmail.com
LE THI THUY
Affiliation:
Department of Mathematics, Hanoi Electric Power University, 235 Hoang Quoc Viet, Tu Liem, Hanoi, Vietnam e-mail: thuylephuong@gmail.com
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Abstract

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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).

Keywords

37L3035B4135K6535D30
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 55 , Issue 2 , May 2013 , pp. 431 - 448
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013

References

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