Nonlinear Functional Approach to the Study of Systems of Hyperbolic Conservation Laws
DescriptionThe study of conservation laws has a very long history and the earliest mathematical work can be traced back to Euler in 1755 on the study of acoustic waves. And the pioneer work on the nonlinear formulation was given by Riemann in solving the so called Riemann problem. Since then, a lot of progress has been made and this will be briefly described in the next section.From the previous works, onr can notice that the approach based on the construction of some nonlinear functionals has been proved to be robust in the study of the well-posedness theories for hyperbolic conservation laws, especially for the one space dimensional problems. One of the most famous functionals is the Glimm functional introduced by Glimm in his celebrated paper for the global existence of entropy solutions with small total variation.In this project, the researchers are going to work on the following two problems by using the nonlinear functional approach. The first problem is about the generalized entropy functional for general scalar hyperbolic conservation laws. And the other one is about the convergence rate of the vanishing viscosity limit for general systems of hyperbolic conservation laws. These two problems are among the most basic and unsolved problems for one space dimensional hyperbolic conservation laws.
|Effective start/end date
|1/04/09 → 18/01/10