Global attractors in stronger norms for a class of parabolic systems with nonlinear boundary conditions

Details Global attractors in stronger norms for a class of parabolic systems with nonlinear boundary conditions Global attractors in stronger norms for a class of parabolic systems with nonlinear boundary conditions

2012-02-17

arxiv.org/abs/1202.3867v1

Mathematics

Analysis of PDEs

This is a preprint version. Published in Nonlinear Analysis 75 (2012) 2922-2935

Scientific paper

For a class of quasilinear parabolic systems with nonlinear Robin boundary conditions we construct a compact local solution semiflow in a nonlinear phase space of high regularity. We further show that a priori estimates in lower norms are sufficient for the existence of a global attractor in this phase space. The approach relies on maximal $L_p$-regularity with temporal weights for the linearized problem. An inherent smoothing effect due to the weights is employed for gradient estimates. In several applications we can improve the convergence to an attractor by one regularity level.

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