Inviscid Burgers' equation:
Viscous Burgers' equation:
The correct physical behaviour is determined adopting the vanishing viscosity approach
The inviscid equation is a model of the viscous one valid only
for small and smooth
If the initial data is smooth and very small the term
is negligible before the wave begins to break. The
solutions to both PDEs look identical
As the wave begins to break the term grows much faster that
the
term and the rhs begins to play a role
This term keeps the solution smooth for all time preventing the breakdown of solutions that occurs for the hyperbolic problem