I will discuss the existence and properties of small-scaledependent shock waves to nonlinear hyperbolic systems, with anemphasis on the theory of nonclassical entropy solutionsinvolving undercompressive shocks. Regularization-sensitivestructures often arise in continuum physics, especially inflows of complex fluids or solids. The so-called kinet...
Creator:
LeFloch, Philippe G. (Université de Paris VI (Pierre et Marie Curie))
Created:
2009-07-23
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Elastic materials exhibit qualitatively different responses to different kinematic boundary conditions or body forces. As a first step towards understanding the related evolutionary problem, one studies the minimizers of an appropriate nonlinear elastic energy functional.We shall give an overview of recent results, rigorously deriving 2d elastic...
Creator:
Lewicka, Marta (University of Minnesota, Twin Cities)
Created:
2009-07-23
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
In this talk we discuss discretization based dispersive-dissipative regularization of mixed type systems and derive the resulting closure conditions known as kinetic relations. Algebraic kinetic relations link velocities of the undercompressed jump discontinuities with the corresponding driving forces and are widely used to model dynamical respo...
Creator:
Truskinovsky, Lev (École Polytechnique)
Created:
2009-07-22
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
It will be reviewed briefly various physical models leading to adescription based on Quantum Hydrodynamics: Superfluidity, BEC,superconductivity, semiconductors and there will be recalled variousderivations of the PDE system.The main result (joint with P. Antonelli) shows the global existenceof 'irrotational' weak solutions withthe sole assumpti...
Creator:
Marcati, Pierangelo (Università di L'Aquila)
Created:
2009-07-22
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.
Several models have been proposed in order to describe cell communities self-organisation. One of them consists in coupling a multidimensional scalar conservation law with an elliptic equation which gradient determines the flux in the conservation law. In dimension larger than 1, the model looses all nice properties of hyperbolic conservation la...
Creator:
Perthame, Benoit (Université de Paris VI (Pierre et Marie Curie))
Created:
2009-07-21
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We show that, for a model system of compressible fluid flow in the upper half space of the plane, curves which intersect the boundary and across which the initial density is discontinuous become tangent to the boundary instantaneously in time. This result is closely related to the instantaneous formation of cusps in two-dimensional incompressibl...
Creator:
Hoff, David (Indiana University)
Created:
2009-07-21
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Some recent research progresses on the multi-dimensionalcompressible Euler equations will be reviewed. In particular, thetransonic flows past an obstacle such as an airfoil, and theisometric embeddings in geometry will be discussed. The talk is basedon the joint works with Gui-Qiang Chen and Marshall Slemrod.
Creator:
Wang, Dehua (University of Pittsburgh)
Created:
2009-07-21
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.