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 2x+f(t). We also present the initial value problem solution for the case with a constant forcing term to compare with the known result.
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