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Exact solutions for a forced Burgers equation with a linear external force

Author

Listed:
  • Zola, R.S.
  • Dias, J.C.
  • Lenzi, E.K.
  • Evangelista, L.R.
  • Lenzi, M.K.
  • da Silva, L.R.

Abstract

We investigate the solutions of the Burgers equation ∂tu(x,t)=D∂x2u(x,t)−∂x[F(x,t)u(x,t)]−κu(x,t)∂xu(x,t)+Φ(x,t), where F(x,t) is an external force and Φ(x,t) represents a forcing term. This equation is first analyzed in the absence of the forcing term by taking F(x,t)=k1(t)−k2(t)x into account. For this case, the solution obtained extends the usual one present in the Ornstein–Uhlenbeck process and depending on the choice of k1(t) and k2(t) it can present a stationary state or an anomalous spreading. Afterwards, the forcing terms Φ(x,t)=Φ1(t)+Φ2(t)x and Φ(x,t)=Φ3x−Φ4/x3 are incorporated in the previous analysis and exact solutions are obtained for both cases.

Suggested Citation

  • Zola, R.S. & Dias, J.C. & Lenzi, E.K. & Evangelista, L.R. & Lenzi, M.K. & da Silva, L.R., 2008. "Exact solutions for a forced Burgers equation with a linear external force," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(12), pages 2690-2696.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:12:p:2690-2696
    DOI: 10.1016/j.physa.2008.01.080
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    Cited by:

    1. Guo, Gang & Li, Kun & Wang, Yuhui, 2015. "Exact solutions of a modified fractional diffusion equation in the finite and semi-infinite domains," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 193-201.
    2. Pereira, Enrique & Suazo, Erwin & Trespalacios, Jessica, 2018. "Riccati–Ermakov systems and explicit solutions for variable coefficient reaction–diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 278-296.

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