Diffusion equation

1. Feb 24, 2016

Dassinia

1. The problem statement, all variables and given/known data
Hello, I don't understand the solution of an exercise

Let P(x) be a continuous function such that |P(x)|≤Ceax² .
Show that formula (8) for the solution of the diffusion equation makes sense for 0 < t < 1/(4ak), but not necessarily for larger t.

2. Relevant equations
Equation (8) refers to
u(x,t)=1/√(4*pi*k*t) ∫ e-(x-y)²/4ktP(y) dy
3. The attempt at a solution
The solution just says that

I don't understand how they conclude ? I don't see why we have 0 < t < 1/(4ak)

Thanks

2. Feb 24, 2016

vela

Staff Emeritus
Consider the sign of the $y^2$ term in the exponent. What has to be true for the integral to converge?

3. Feb 25, 2016

Dassinia

I see, thanks !