Fourier Transform

Fourier Transform Let u(:c,t) solve the partial differential equation c'3;u=8,2,u-u, a:E1R, t >0, with initial condition u(a:,0) = v(a:) for (E E R. Furthermore, denote by 11 = J-' the Fourier transform of u with respect to 9:. Show that 12 satisfies the equation ata = -(k2 + 1)a with initial condition 1l(k,O) = 0(k) = }'{v}. Find the solution 11 of the equation in Fourier space and thereby the solution u of the original equation. PLACE THIS ORDER OR A SIMILAR ORDER WITH US TODAY AND GET AN AMAZING DISCOUNT :)