On quasilinear parabolic evolution equations in weighted Lp-spaces II

By Jeremy LeCrone, Jan Pruess, M. Wilke. 2009

85 citations recorded by the source corpus.

Our study of abstract quasi-linear parabolic problems in time-weighted Lp-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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/caa8fe060dcd936406a12ff95963db0aaefc399c

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In Applied Mathematics

1. Mark Veraar
2. C. Gallarati
3. M. Meyries
4. J. V. Neerven
5. Lutz Weis

In Computational Theory and Mathematics

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In Numerical Analysis

1. Mark Veraar
2. M. Meyries

Citations in the corpus

• Traces and embeddings of anisotropic function spaces (2012, unknown): “ be used to show an intrinsic smoothing effect of the parabolic problem and compactness of the semiflow, which is an important property for the investigation of the long-time behavior of solutions (see [23, 32]). As it turns out, power weights are not only important for the applications. They are in f”
• Sharp embedding results for spaces of smooth functions with power weights (2011, methodology): “oefficients or domains with a nonsmooth geometry (see e.g. [4, 22, 26, 42]). For evolution equations, power weights in time play an important role in order to obtain results for rough initial data (see [11, 20, 25, 31]). In addition, here one is naturally confronted with vector-valued spaces. Our work”
• Maximal Regularity for Non-autonomous Equations with Measurable Dependence on Time (2014, background): “ to create compactness properties. At the same time, the regularity properties of the solution to (4.15) for t>0 are unchanged. For more details and applications to evolution equations we refer to [36, 56, 64, 68, 69, 79]. Example 4.16. Assume v(t) = tα with α∈ (−1,p− 1). Then v∈ Ap and Xv,p = (X”