QUASILINEAR PARABOLIC EQUATIONS WITH NONLOCAL BOUNDARY COND

Forum for the GRE subject test in mathematics.
mathmai
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QUASILINEAR PARABOLIC EQUATIONS WITH NONLOCAL BOUNDARY COND

Postby mathmai » Tue Apr 17, 2012 5:20 pm

I want to ask about the articl: http://ejde.math.txstate.edu/Volumes/2011/18/chen.pdf

In the lamma4.4 and 4.5 and 4.6 the required convergence is strong but in the proof she indicate just the weak convergence so why?
what does it mean $L^q(0,T;\ H^{-r}(\Omega))$ or how can I read it mathematicaly?



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