This series of four lectures will provide an introductionto multidimensional conservation laws, along with a perspective on alist of open problems. The main topics will include: Prototypes and Basic Features/Phenomena Multidimensional Models Multidimensional Steady Problems Multidimensional Self-Similar Problems Compressible Vortex Sheets and Re...
Creator:
Chen, Gui-Qiang G. (Northwestern University)
Created:
2009-07-13
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Singular limits in the theory of partial differential equationsrepresent a class of problems, where some parameters in the equations becomesmall or infinitely large. We discuss the singular limits arising in the scaleanalysis of energetically isolated fluid systems. In particular,the following topics are addressed: functional analytic framework ...
Creator:
Feireisl, Eduard (Czech Academy of Sciences (AVÄŒR))
Created:
2009-07-13
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
This set of lectures will provide a basic introduction to hyperbolic systems of conservation laws in one space dimension. The main topics covered will be: Meaning of the conservation equations and definition of weak solutions.Shocks, Rankine-Hugoniot equations and admissibilityconditions.The Riemann problem. Wave interaction estimates.Weak solut...
Creator:
Bressan, Alberto (The Pennsylvania State University)
Created:
2009-07-13
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
I am planning to convey a feel for the area by touching upon its history, its general features, the current directions, etc., paving the way for the more technical lectures by others.
Creator:
Dafermos, Constantine (Brown University)
Created:
2009-07-13
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.