A mathematical model for the transport of SO2 gas into snow by modelcular diffus

Question

A mathematical model for the transport of SO2 gas into snow by modelcular diffusion. The governing partial differential equation is

   ?C?t=D(?2C?x2?a2C)   

where C is the concentration of SO2 as a function of x(depth of snow) and time; D is a diffusion constant. a^2 is also a constant.

If the snow is deep, x has a semi-infinite interval for x and

limx??C(x,t)=0   .

Also,

C(0,t)=0,0<x   

   C(x,0)=0,0<x   

a. Find a steady state solusion v(x) that satisfies the partial differential equation and the boundary conditions.

b. State the problem to be satisfies by the transient w(x,t) = C(x,t) - v(x).

c. Solve the transient.

Explanation / Answer

The equation is not clear.

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