Differential Equation
Hey, I'm somewhat stumped on how to tackle this differential equation. Any advice is really appreciated.
The equation reads
(1/v)*D(C)/Dt - (3/2)*D(C)/Dy = a*D^2(C)/Dy^2,
where v and a are constants, and D^n(C)/Dy^n is the n-th derivative of C with respect to y.
Here y = ln(R).
At t=0, we have C(R,t=0) = B*delta(R-R_o) , where delta() is the dirac delta function. It says setting
X = y + (3/2)*v*t
may also help. The problem also gives that the general solution to
D^2(u)/Dx^2 - D(u)/Dt = 0 is
u(x,t) = (1/sqrt(4pi*t))Integral( u(x,0) exp(-(x-g)^2/(4t) )dg integrated from -infty to infty.
:S
The equation reads
(1/v)*D(C)/Dt - (3/2)*D(C)/Dy = a*D^2(C)/Dy^2,
where v and a are constants, and D^n(C)/Dy^n is the n-th derivative of C with respect to y.
Here y = ln(R).
At t=0, we have C(R,t=0) = B*delta(R-R_o) , where delta() is the dirac delta function. It says setting
X = y + (3/2)*v*t
may also help. The problem also gives that the general solution to
D^2(u)/Dx^2 - D(u)/Dt = 0 is
u(x,t) = (1/sqrt(4pi*t))Integral( u(x,0) exp(-(x-g)^2/(4t) )dg integrated from -infty to infty.
:S