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Math Help - Minimum of Functional

  1. #1
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    Post Minimum of Functional

    Find an upper bound for the minimum of the functional
     J\{y\} = \int\begin{array}{cc}1\\0\end{array} y^2 y'^2 dx
    subject to y(0)=0 and y(1)=1 using te trial functions
    y_\epsilon(x)=x^\epsilon with  \epsilon > 1/4. Justify your argument.

    Thanks in advance
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  2. #2
    A Plied Mathematician
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    So, what have you done so far?

    Incidentally, while I grant you that this is calculus of variations, it really belongs in the Advanced Applied Mathematics forum. If you report your own post and ask the mods to move it, they'll do that for you. That's the correct way to move the post.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by pdnhan View Post
    Find an upper bound for the minimum of the functional
     J\{y\} = \int\begin{array}{cc}1\\0\end{array} y^2 y'^2 dx
    subject to y(0)=0 and y(1)=1 using te trial functions
    y_\epsilon(x)=x^\epsilon with  \epsilon > 1/4. Justify your argument.

    Thanks in advance
    If you minimise J\{y_{\epsilon}\} wrt $$ \epsilon you will have an upper bound on the mininmum of the functional. This is a standard (constrained) minimisation problem.

    CB
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Ackbeet View Post
    So, what have you done so far?

    Incidentally, while I grant you that this is calculus of variations, it really belongs in the Advanced Applied Mathematics forum. If you report your own post and ask the mods to move it, they'll do that for you. That's the correct way to move the post.
    'fraid not, this is a plain old calculus problem, when interpreted.

    CB
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  5. #5
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    I got it now, thank you very much!
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