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.
Recommended Citation
Lecrone, Jeremy, and Gieri Simonett. “On Quasilinear Parabolic Equations and Continuous Maximal Regularity.” Evolution Equations and Control Theory 9, no. 1 (March 2020): 61–86. https://doi.org/10.3934/eect.2020017.
