Having Alot of Trouble

Homework Statement

Let u(x,t) satisfy

Homework Equations

($$\partial$$u/$$\partial$$t) = ($$\partial$$$$^{2}$$u/$$\partial$$x$$^{2}$$)........(0<x<1,t>0)

u(0,t)=u(1,t)=0........(t$$\geq$$0)

u(x,0)=f(x)........(o$$\leq$$x$$\leq$$1),

where f$$\in$$C[0.1] show that for any T$$\geq$$0

$$\int$$ from 0..1 (u(x,T))$$^{2}$$dx $$\leq$$ $$\int$$ from 0..1 (f(x))$$^{2}$$dx

not sure

The Attempt at a Solution

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berkeman
Mentor
That's 3 posts and no work shown on any one of them. You *must* show an attempt at a solution, or we cannot be of help to you. Please click on the "Rules" link at the top of the page.

im sorry, im obviously knew to this forum....

For this problem, im trying to use the identity as follows

2u(($$\partial$$u/$$\partial$$t)-($$\partial$$$$^{2}$$u/$$\partial$$x$$^{2}$$)) = ($$\partial$$u$$^{2}$$/$$\partial$$t)-($$\partial$$/$$\partial$$x)*(u*($$\partial$$u/$$\partial$$x))+2*($$\partial$$u/$$\partial$$x)$$^{2}$$

Dick