The shock wave solution to the Riemann problem for the Burgers equation with the linear forcing term

Abstract

In this note, the Riemann problem for the inviscid Burgers equation with a linear forcing term is considered. The shock wave solution is obtained by combining the generalized Rankine–Hugoniot jump condition together with the method of characteristics, which reflects the impact of the inhomogeneous forcing term on the shock front. In addition, some interesting phenomena are also observed during the construction process of Riemann solution.

Keywords:

• Burgers equation
• linear forcing term
• Riemann problem
• shock front
• generalized Rankine–Hugoniot condition
• method of characteristics

AMS Subject Classifications:

• 35L65
• 35L67
• 35B25
• 90B20

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant number 11441002], [grant number 11271176]; the Shandong Provincial Natural Science Foundation [grant number ZR2014AM024].