Quasilinear parabolic equation and its applications to fourth order equations with rough initial data
Vol. 19 (2012), No. 4, Page 507–532.
Asai, Tomoro
Quasilinear parabolic equation and its applications to fourth order equations with rough initial data
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Abstract:
The main part of this paper is devoted to establishing existence and uniqueness results for a class of abstract quasilinear parabolic equations by using the theory of continuous maximal regularity. The abstract results are then applied to some fourth order quasilinear parabolic equations (such as the surface diffusion flow and the Willmore flow) with rough initial data.
Mathematics Subject Classification (2010): Primary 35K90; Secondary 35K59.
Mathematical Reviews Number: MR3086745
Received: 2011-07-04
