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Math Help - Existence of solutions for quasilinear parabolic equations

  1. #1
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    Existence of solutions for quasilinear parabolic equations

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

    try to enter to this link which is an article about [EXISTENCE OF SOLUTIONS FOR QUASILINEAR PARABOLIC
    EQUATIONS WITH NONLOCAL BOUNDARY CONDITIONS], I have question in the page 3 section 3:
    the expression:
    [We need a priori estimates that permit us to extend the solution to the whole
    domain [0, T].] what does it mean this expression mathematicaly?????
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  2. #2
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    Re: Existence of solutions for quasilinear parabolic equations

    The formulas used require the assumption that " f\in L^p(0, T;L^p(\Omega))". The "a-priori estimates" (initial estimates of the values of f) are to make sure that f satisfies that.
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  3. #3
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    alger
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    Re: Existence of solutions for quasilinear parabolic equations

    But the priori estimates in this articl (page 5) are all depend in u not f how this??

    please tell me why u mention f here and what's the relation between these values u and f....?
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