Our study of abstract quasi-linear parabolic problems in time-weighted L_p-spaces, begun in 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 definitive version is available at: http://link.springer.com/article/10.1007/s00028-014-0226-6
Full Citation: LeCrone, Jeremy, Jan Prüss, and Mathias Wilke. "On Quasilinear Parabolic Evolution Equations in Weighted Lp-Spaces II." Journal of Evolution Equations 14, no. 3 (September, 2014):509-533. doi:10.1007/s00028-014-0226-6.
LeCrone, Jeremy; Wilke, Mathias; and Prüss, Jan, "On Quasilinear Parabolic Evolution Equations in Weighted Lp-Spaces II" (2014). Math and Computer Science Faculty Publications. 160.