A question on Laplace eq.

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1 total messages Started by jtrsmith Thu, 03 Sep 1992 17:29

#55

Author: jtrsmith
Date: Thu, 03 Sep 1992 17:29

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Hi, Sirs,
I have a question about if a Laplace equation 

       div grad T = 0       in a smooth enough domain,

is well-posed under following boundary condition:

    - dT/dn = a ( T*T*T*T - c),  on the domain boundary, 

    (note: T*T*T*T means T to the fourth power.)
where n is in the direction of outward unit normal along the boundary,
a, c is constant, and  a>0.

This boundary is equivalent to a radiation along boundary; heat
conducted from the domain is radiated to out side environment.

Can anybody prove that the problem is well-posed? 

If possible, please reply to this account directly. Thanks.

JTR Smith

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