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Mathematics > Analysis of PDEs

arXiv:1808.01032 (math)
[Submitted on 2 Aug 2018]

Title:On quasilinear parabolic equations and continuous maximal regularity

Authors:Jeremy LeCrone, Gieri Simonett
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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.
Comments: 27 pages
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:1808.01032 [math.AP]
  (or arXiv:1808.01032v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1808.01032

Submission history

From: Jeremy LeCrone [view email]
[v1] Thu, 2 Aug 2018 21:52:37 UTC (29 KB)
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