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Exact solutions for a forced Burgers equation with a linear external force |
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| Authors: | RS Zola EK Lenzi LR Evangelista LR da Silva |
| Institution: | a Departamento de Física, Universidade Estadual de Maringá, Avenida Colombo, 5790-87020-900 Maringá, Paraná, Brazil b Departamento de Engenharia Química, Universidade Federal do Paraná, Setor de Tecnologia - Jardim das Américas, Caixa Postal 19011, 81531-990, Curitiba, Paraná, Brazil c Departamento de Física, Universidade Federal do Rio Grande do Norte, 59078-970 Natal-RN, Brazil |
| Abstract: | We investigate the solutions of the Burgers equation  , 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: | 02 50 -r 05 40 -a 05 90 +m |
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