Abstract
Our study of abstract quasi-linear parabolic problems in time-weighted L p -spaces, begun in Köhne et al. (J Evol Equ 10:443–463, 2010), is extended in this paper to include singular lower-order terms, while keeping low initial regularity. The results are applied to reaction-diffusion problems, including Maxwell–Stefan diffusion, and to geometric evolution equations like the surface diffusion flow or the Willmore flow. The method presented here will be applicable to other parabolic systems, including free boundary problems.
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The work of Jeremy LeCrone was partially supported by a grant from the Simons Foundation (#245959 to G. Simonett).
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LeCrone, J., Prüss, J. & Wilke, M. On quasilinear parabolic evolution equations in weighted L p -spaces II. J. Evol. Equ. 14, 509–533 (2014). https://doi.org/10.1007/s00028-014-0226-6
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DOI: https://doi.org/10.1007/s00028-014-0226-6