- #1
kingwinner
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Homework Statement
Let u(x1,x2,...,xn,t) be a function of n+1 variables. Let D be an open, bounded, connected set in R^n(with respect to x1,...,xn) and all functions are smooth.
Claim 1:
If u=0 on the boundary of D, then ut=0 on the boundary of D.
Let u(x,y) be a function of 2 variables.
Claim 2:
If u(x,0)=0, then ux(x,0)=0.
I don't understand either of the claims above.
Homework Equations
N/A
The Attempt at a Solution
I really can't think of a reason why these are true. Also, I cannot check it directly by differentiating u with respect to t (or x) because I don't even know what the function u is. I was only given that u is 0 at some very specific points.
Can someone please explain or prove it?
Any help is appreciated! :)
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