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Attractors for a class of doubly nonlinear parabolic systems. (English) Zbl 1085.35064
Summary: In this paper, we establish the existence and boundedness of solutions of a doubly nonlinear parabolic system. We also obtain the existence of a global attractor and the regularity property for this attractor in $$\left[ L^{\infty }(\Omega )\right] ^{2}$$ and $${\displaystyle \prod_{i=1}^{2}}{B_{\infty }^{1+\sigma _{i},p_{i}}( \Omega )}$$.

##### MSC:
 35K50 Systems of parabolic equations, boundary value problems (MSC2000) 35K55 Nonlinear parabolic equations 35K57 Reaction-diffusion equations 35K65 Degenerate parabolic equations 35B40 Asymptotic behavior of solutions to PDEs 35B45 A priori estimates in context of PDEs
##### Keywords:
$$p$$-Laplacian; global attractor; asymptotic behaviour
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