- #1
modeiry88
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Homework Statement
Let u(x,t) satisfy
Homework Equations
([tex]\partial[/tex]u/[tex]\partial[/tex]t) = ([tex]\partial[/tex][tex]^{2}[/tex]u/[tex]\partial[/tex]x[tex]^{2}[/tex])...(0<x<1,t>0)
u(0,t)=u(1,t)=0...(t[tex]\geq[/tex]0)
u(x,0)=f(x)...(o[tex]\leq[/tex]x[tex]\leq[/tex]1),
where f[tex]\in[/tex]C[0.1] show that for any T[tex]\geq[/tex]0
[tex]\int[/tex] from 0..1 (u(x,T))[tex]^{2}[/tex]dx [tex]\leq[/tex] [tex]\int[/tex] from 0..1 (f(x))[tex]^{2}[/tex]dx
The Attempt at a Solution
not sure