DOI

https://doi.org/10.3934/eect.2020017

Abstract

We consider a class of abstract quasilinear parabolic problems with lower–order terms exhibiting a prescribed singular structure. We prove well–posedness and Lipschitz continuity of associated semiflows. Moreover, we investigate global existence of solutions and we extend the generalized principle of linearized stability to settings with initial values in critical spaces. These general results are applied to the surface diffusion flow in various settings.

Document Type

Post-print Article

Publication Date

3-2020

Publisher Statement

Copyright © 2021, American Institute of Mathematical Sciences.

DOI: https://doi.org/10.3934/eect.2020017

The definitive version is available at: Evolution Equations and Control Theory 9, no. 1.

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Mathematics Commons

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