PDE:Cauchy Problem for Heat Equation

  • #1

Homework Statement

Solve the Cauchy problem
ut =kuxx, x ∈ R, t>0, u(x, 0) = φ(x),
for the following initial conditions.
(a) φ(x)=1if |x|<1 and φ(x)=0 if |x|>1.
Write the solutions in terms of the erf function.

Homework Equations

u(x,t)=∫G(x-y,t)*φ(y)dy from -∞, to ∞
where G(x,t) is the heat kernel or fundamental solution to heat equation.

The Attempt at a Solution

I am not sure if this correct:
Separate the integral into different parts according above condition and then plugin φ(x) value for φ(y) in the integral. And then proceed from there on

Answers and Replies

  • #2
Science Advisor
Insights Author
Gold Member
Sounds good to me. Just do it!