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April 30, 2009, 13:08 
heat conduction problem  well posedness

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I was wondering if the following problem is well posed:
T_t = (a^2) T_xx, T(x,t) = temperature, 0 < x < 1, t > 0. T(x,0) = f(x), T(0,t) = g(t), T_x(0,t) = h(t). Instead of the last condition on T_x, if I had T(1,t) = e(t), then it is well posed and has a unique solution. Because the temperature and heat flux is specified on one end, I am wondering how one gets a SturmLiouville problem in x, in this case. Thanks for all the help. 

May 1, 2009, 16:03 

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heat conduction, well posed 
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