2012-07-20 11:41:42 8 Comments

Has anyone read G. DaPrato and P. Grisvard *Equations d'evolution abstraites nonlineaires de type parabolique*?

It's not available in my library. I am wondering if it's worth me acquiring it: is it all in French? I only know English. Are there articles/papers that cover the same material and that are more easily available? I'm particularly interested in the proof for local existence of a nonlinear parabolic PDE that the authors treat by some semigroup approach (I believe) which makes continuous dependence on parameters easy to show. Thanks.

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## 1 comments

## @Willie Wong 2012-07-20 12:10:33

I haven't; but someone did.

`:-)`

Yes

It depends on which results you are looking for. It maybe that the result that you need is already contained in some previous work (some of which are in English). The following is translated/excerpted from the first page of the article.

For existence of weak solutions (using monotone operators), the method in the paper is similar to those of references 15, 14, 8, 7, 4.

(All references refer to the references in the paper, which you can see on this page.)

For classical solutions, the basic technique is that of references 21, 14, 12, 20, and 19. The main difference is that in the DaPrato-Grisvard article, the equation is not assumed to be a perturbation of a linear equation, which they achieve by developing some new interpolation spaces.