Summary
In this paper some aspects of the asymptotic behavior of solutions of quasilinear (generally nonautonomous) parabolic equations are considered. Specifically a result of convergence to a stationary state is given and, under more restrictive conditions, some sharper descriptions of converging solutions are obtained. Finally a saddle point situation is examined. The employed techniques are abstract and inspired by the papers of Sobolevskii and Da Prato-Grisvard.
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Guidetti, D. Convergence to a stationary state and stability for solutions of quasilinear parabolic equations. Annali di Matematica pura ed applicata 151, 331–358 (1988). https://doi.org/10.1007/BF01762803
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DOI: https://doi.org/10.1007/BF01762803