SYNOPSIS (ISBN: 978-972-8826-22-2) We are concerned by nonlinear conservation laws and claim a realistic, well established analytical setting, based on energy methods. Scalar models are multi-space dimensional and rely all known physically relevant solutions, both classical and nonclassical. Main issue is about “when can we work with hyperbolic (simplified) models? Failure, reliability and integrity?” SYNOPSIS (ISBN: 978-972-8826-21-5) We are concerned with nonlinear conservation laws and we are aiming for a realistic multispace dimensional framework. The main issue we are interested in is the following “when can we use hyperbolic (simplified) models?” and to answer it, we study zero diffusion-dispersion limits. While our proofs establish integrity, the major emphasis is on reliability and failure. In particular, we look to all known physically relevant solutions, both classical and nonclassical. The techniques we use depend upon an analytical setting on measure-valued function theory and are energy based methods.