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.
Copyright © 2021, American Institute of Mathematical Sciences.
The definitive version is available at: Evolution Equations and Control Theory 9, no. 1.
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.