Geodesic
Non-local quasi-linear parabolic equations
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 60 (2005) no. 6, pp. 1021-1033

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This is a survey of the most common approaches to quasi-linear parabolic evolution equations, a discussion of their advantages and drawbacks, and a presentation of an entirely new approach based on maximal $L_p$ regularity. The general results here apply, above all, to parabolic initial-boundary value problems that are non-local in time. This is illustrated by indicating their relevance for quasi-linear parabolic equations with memory and, in particular, for time-regularized versions of the Perona–Malik equation of image processing. 
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     author = {H. Amann},
     title = {Non-local quasi-linear parabolic equations},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_2005_60_6_a2/}
}
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H. Amann. Non-local quasi-linear parabolic equations. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 60 (2005) no. 6, pp. 1021-1033. http://geodesic.mathdoc.fr/item/RM_2005_60_6_a2/