Quaslinear equation

par hilda4 Jeu 10 Mai - 22:34

you can please check the pdf baili chen :EXISTENCE OF SOLUTIONS FOR QUASILINEAR PARABOLIC EQUATIONS WITH NONLOCAL BOUNDARY CONDITIONS

http://ejde.math.txstate.edu/Volumes/2011/18/chen.pdf

,Can we say that the boundary integral conditions= the nonlocal boundary condition?!!
,When the generalized solution = the weak solution?
,What's the norm of the sobolev space H^{-r} and how we can say u_{m}^{p-2}u_{m} \in L^{q}(0,T;H^{-r})(\omega))?
,In all the lemma 4.4....4.7 they try to use the norm in H^{-r})(\omega) why?
,In the article page 5 when it wrote:
Under assumption (A1)-(A5), we have the following a priori estimates:
(B).............
(C) .........
(D).........
how she deduced this ??I mean (B)(C)(D)

If u don't get the message in English tell me to translate it to French..