Hyperbolic PDE

2011 5 27
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Hi,
I'm trying to solve the following advection diffusion problem.
dT/dt= -A(t)*dT/dx - B*T^(3/2)*(T-C(t))
where T(0,t)= 498; T(x,0)= 520;
Is there any built-in function in Matlab that I can get help with this problem?
Luke

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Walter Roberson
Walter Roberson 2011-5-27

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Would it be correct that the more explicit version of your equation would be
diff(T(x, t), t) = -A(t)*(diff(T(x, t), x))-B*T(x, t)^(3/2)*(T(x, t)-C(t))
If so then Maple's pdsolve() believes there is no solution.
Consider your boundary conditions at x=0, t=0. According to your first boundary condition, T(0,0)=498, but according to your second boundary condition, T(0,0)=520 . That is a contradiction and hence there is no solution.

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