SIAM 2002 challenge #8

8. A square plate [-1, 1] × [-1, 1] is at temperature u = 0. At time t = 0 the temperature is increased to u = 5 along one of the four sides while being held at u = 0 along the other three sides, and heat then flows into the plate according to u_t = Du. When does the temperature reach u = 1 at the center of the plate?

Bernard's familiarity with the conduction equation (with zero heat generation) in 2-D,


    ðT             ð²T   ð²T
    --  =  (const) --- + ---
    ðt             ðx²   ðy²

enabled us to interpret the notation in the statement of this problem.

Bernard B. Beard's 0.5 megabyte pdf combined all our solutions into one file. I've extracted the pages covering his solution of #8, it came out as a postscript file. The characters r that appear above a few of the letters were vector arrows in the original. Hope to have a better version in a few days.

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