- #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 u

_{t}=0 on the boundary of D.

Let u(x,y) be a function of 2 variables.

Claim 2:

If u(x,0)=0, then u

_{x}(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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