Stochastic solution of nonlinear and nonhomogeneous evolution problems by a differential Kolmogorov equation
نویسنده
چکیده
A large class of physically important nonlinear and nonhomogeneous evolution problems, characterized by advection-like and diffusion-like processes, can be usefully studied by a time-differential form of Kolmogorov’s solution of the backward-time Fokker-Planck equation. The differential solution embodies an integral representation theorem by which any physical or mathematical entity satisfying a generalized nonhomogeneous advection-diffusion equation can be calculated incrementally in time. The utility of the approach for tackling nonlinear problems is illustrated via solution of the noise-free Burgers and related Kardar-Parisi-Zhang (KPZ) equations where it is shown that the differential Kolmogorov solution encompasses, and allows derivation of, the classical Cole-Hopf ∗Address: Mechanical Engineering & Engineering Science, UNC-Charlotte, 9201 University City Blvd, Charlotte, NC 28223-0001. Email: [email protected]; Phone: 704-687-8336; Fax: 704-687-8345
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