ABSTRACT
For initial conditions not of Riemann type, in particular those with integrable data, or for more general random initial conditions, obtaining solutions of the conservations law is not a simple matter, even in approximate fashion. The usual approach then is to consider a parabolic regularization (the viscosity method) by considering the nonlinear diffusion equations https://www.w3.org/1998/Math/MathML"> ∂ u ∂ t + ∂ H ( u ) ∂ x = ϵ L u , u ( 0 , x ) = u 0 ( x ) , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003216759/e7d667ff-34e1-4696-9d72-d545d9499230/content/equ0115-01.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
