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.

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:

Chen, Gui-Qiang G. (Northwestern University)

Created:

2009-07-17

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:

Chen, Gui-Qiang G. (Northwestern University)

Created:

2009-07-18

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.

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:

2009-07-14

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:

2009-07-16

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:

2009-07-17

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

In this talk we consider a conservation law (or a system of conservationlaws) on a network consisting in a finite number of arcs and vertices.This setting is justified by various applications, such as car traffic,gas pipelines, data networks, supply chains, blood circulation and so on.The key point in the extension of conservation laws on networ...

Creator:

Garavello, Mauro (Università del Piemonte Orientale 'Amedeo Avogadro')

Created:

2009-07-30

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.

The Kriess-Sakamoto theory for the well-posedness of hyperbolic IBVPs and the Majda theory for shock-wave stability apply under the assumption that a suitable Lopatinski condition holds uniformly. The failure of uniformity is associated with the presence of surface waves on the boundary or discontinuity. We will derive asymptotic equations for '...

Creator:

Hunter, John K. (University of California, Davis)

Created:

2009-07-27

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

In this course we will give an introduction to conservativeshort capturing numerical methods for solving multi-dimensionalsystems of conservation laws. High order accurate finitedifference, finite volume and discontinuous Galerkin finiteelement methods will be covered. We will start with thebasic algorithm issues in a simple scalar one dimension...

Creator:

Shu, Chi-Wang (Brown University)

Created:

2009-07-15

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:

Shu, Chi-Wang (Brown University)

Created:

2009-07-17

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

We provide a bird's eye view of a selected topics in approximate solution of nonlinear conservation laws and related time dependent equations. We begin with a discussion on regularity spaces in theory and computation. We will continue with a presentation of the class of high-resolution central schemes. We will discuss the issue of entropy stabil...

Creator:

Tadmor, Eitan (University of Maryland)

Created:

2009-07-14

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Motivated by the problem of symmetric collapsing gas-dynamical shocks wepresent a scalar toy model that captures blowup of focusing waves. This modelis simple enough to allow for explicit calculations, and we study some solutions indetail. As a scalar model it does not describe reflection of waves and this necessitatesa new concept of weak solut...

Creator:

Jenssen, Helge Kristian (The Pennsylvania State University)

Created:

2009-07-27

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

In his celebrated thesis, S. Kawashima gave a framework for the analysis of the Cauchy problem for nonlinear viscous systems of conservation laws. Some assumptions are quite natural, while other ones are mysterious and require cumbersome calculations. We clarify the situation, by introducing a set of assumption which is natural and very easy to ...

Creator:

Serre, Denis (École Normale Supérieure de Lyon)

Created:

2009-07-22

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

Given a model based on a conservation law, we study how the solutiondepends from the initial/boundary datum, from the flow and fromvarious constraints. With this tool, several control problems can beaddressed and the existence of an optimal control can beproved. Models describing escape dynamics of pedestrians, traffic attoll gates, open canals ...

Creator:

Colombo, Rinaldo Mario (Università di Brescia)

Created:

2009-07-31

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.

The talk will be based on a joint work with L. Ambrosio, G. Crippa and A.Figalli. First, some new well-posedness results for continuity andtransport equations with weakly differentiable velocity fields will bediscussed. These results can be applied to the analysis of a 2 x 2 systemof conservation laws in one space dimension known as the chromato...

Creator:

Spinolo, Laura Valentina (Scuola Normale Superiore)

Created:

2009-07-25

Contributed By:

University of Minnesota, Institute for Mathematics and its Applications.