Entropy and Singular Solutions for Conservation Laws; Pressureless Gas Dynamics and Other Applications
Month: September 2014
Date: September 26--28
Name: Entropy and Singular Solutions for Conservation Laws; Pressureless Gas Dynamics and Other Applications
Location: West Virginia University, Morgantown, West Virginia.
For most of the significant equations of mathematical physics, it is impossible to show the existence of classical solutions even starting out from smooth initial values. On the other hand, if we consider distributional weak solutions, they fail to be unique. To overcome this obstacle, we use the entropy criterion as one of the admissibility criteria compatible with the Second Law of Thermodynamics, to help us single out a unique physically meaningful solution. Recently, the entropy criterion has also been used in connection with systems of pressureless gases to ensure uniqueness of solutions. This arises as a consequence of a deeper connection between scalar Conservation Laws (with rather general flux functions) and Pressureless Gas systems. Despite classical results on existence, uniqueness and stability of entropy solutions for Conservation Laws, there are applications that require the accommodation of more general, uncommon flux functions.