## Having Alot of Trouble

1. The problem statement, all variables and given/known data

Let u(x,t) satisfy

2. Relevant 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

3. The attempt at a solution

not sure
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
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 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)$$^{2}$$

Recognitions:
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