(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I have a 1D diffusion equation as

du/dt = D*d^2u/dx^2-K*u; where D and k = constants

the initial condition is u(t=0)=0

B.C. is u(x=0,t=0)= u0*delta(t); (a pulse like input at x=0 and delta(t)= dirac delta function)

where u = contaminant in a semi infinite slab (0<=x<=inf)

2. Relevant equations

The term (x/t) makes me a bit nervous...Could someone help me fix this Problem?

3. The attempt at a solution

u(x,t) = (u0*exp(-K*t)/sqrt(4*pi*D*t))*(x/t)*exp(-x^2/(4*D*t))

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# 1D diffusion equation

Can you offer guidance or do you also need help?

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