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

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

Physica A: Statistical Mechanics and its Applications, 2008, vol. 387, issue 12, 2690-2696

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.

Keywords: Nonlinear equation; Burgers equation; Solutions (search for similar items in EconPapers)
Date: 2008
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:387:y:2008:i:12:p:2690-2696

DOI: 10.1016/j.physa.2008.01.080

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