Solving a Boundary Value Problem using Fourier Transforms

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Homework Statement



Formally solve the following boundary value problem using Fourier Transforms.

Homework Equations



[tex]\partial[/tex]u/[tex]\partial[/tex]t = ([tex]\partial[/tex][tex]^{2}[/tex]u/[tex]\partial[/tex]x[tex]^{2}[/tex])+([tex]\partial[/tex]u/[tex]\partial[/tex]x)

(-[tex]\infty[/tex]<x<[tex]\infty[/tex],t>0)

u(x,0)=[tex]\Phi[/tex](x)

(-[tex]\infty[/tex]<x<[tex]\infty[/tex])

u(x,t) is bounded for -[tex]\infty[/tex]<x<[tex]\infty[/tex],t[tex]\geq[/tex]0


The Attempt at a Solution



Cannot come up with a solution
 
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