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Thread: Describe the shape of u for times t>3

  1. #1
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    Describe the shape of u for times t>3

    Hello,

    I have a problem from Evans_partial differantial equations. Ch 2.23

    Let S denote the square lying in R x (0,∞)with corners at the points (0,1), (1,2), (0,3), (-1,2). Define


    f(x,t)= -1 for (x,t) ԑ S ∩ {t>x+2}
    1 for (x,t) ԑ S ∩ {t<x+2}
    0 otherwise

    Assume u solves

    utt-uxx=f in R x (0,∞)
    u=0, ut=0 on R x {t=0}

    Describe the shape of u for times t>3.

    (J. G. Kingston, SIAM Review 30 (1988), 645-649)

    I would be appreciated if anyone helpe me. Thank you
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    Re: Describe the shape of u for times t>3

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