Inhomogeneous Burgers Equation and the Feynman-Kac Path Integral
Abstract
By linearizing the inhomogeneous Burgers equation through the Hopf-Cole transformation, we formulate the solution of the initial value problem of the corresponding linear heat type equation using the Feynman-Kac path integral formalism. For illustration, we present the exact solution for the forcing term of the form:
F(x,t)=
ω
2
x+f(t).
We also present the initial value problem solution for the case with a constant forcing term to compare with the known result.