Recent content by modeiry88

im sorry, I am obviously knew to this forum... For this problem, I am trying to use the identity as follows 2u((\partialu/\partialt)-(\partial^{2}u/\partialx^{2})) = (\partialu^{2}/\partialt)-(\partial/\partialx)*(u*(\partialu/\partialx))+2*(\partialu/\partialx)^{2}

Homework Statement Let u(x,t) satisfy Homework Equations (\partialu/\partialt) = (\partial^{2}u/\partialx^{2})...(0<x<1,t>0) u(0,t)=u(1,t)=0...(t\geq0) u(x,0)=f(x)...(o\leqx\leq1), where f\inC[0.1] show that for any T\geq0 \int from 0..1 (u(x,T))^{2}dx \leq \int from...

Homework Statement Formally solve the following boundary value problem using Fourier Transforms. Homework Equations (\partial^{2}u/\partialx^{2})+(\partial^{2}u/\partialy^{2}) = 0 (-\infty<x<\infty,0<y<1) u(x,0)= exp^{-2|x|} (-\infty<x<\infty) u(x,1)=0...

Homework Statement Formally solve the following boundary value problem using Fourier Transforms. Homework Equations \partialu/\partialt = (\partial^{2}u/\partialx^{2})+(\partialu/\partialx) (-\infty<x<\infty,t>0) u(x,0)=\Phi(x) (-\infty<x<\infty) u(x,t) is bounded for...