Burgers' equation is a fundamental partial differential equation from fluid mechanics. It occurs in various areas of applied mathematics, such as modeling of gas dynamics and traffic flow. It is named for Johannes Martinus Burgers (1895–1981).
For a given velocity u and viscosity coefficient, the general form of Burgers' equation (also known as viscous Burgers' equation) is:
- .
When, Burgers' equation becomes the inviscid Burgers' equation:
which is a prototype for equations for which the solution can develop discontinuities (shock waves). The previous equation is the 'advection form' of the Burgers' equation. The 'conservation form' is:
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