ncku-talk2014-02-27

NCTS(South)/ NCKU Math Colloquium

DATE 2014-02-27　16:10-17:00

PLACE R204, 2F, NCTS, NCKU

SPEAKER 洪盟凱教授（中央大學數學系）

TITLE Hyperbolic Resonant Systems of Balance Laws

ABSTRACT In this talk we consider some 2 by 2 and 3 by 3 hyperbolic resonant systems of balance laws arise in fluid dynamics, traffic flows and solid mechanics. We say a system of conservation laws is resonant in some domain if the eigenvalues of Jacobian matrix of the flux coincide in this domain. The existence, uniqueness and properties of the entropy solutions to the Riemann problem is studied. A new entropy wave, which is called the composite elementary waves, is also introduced. The problem related to the global existence of weak solutions for the Cauchy problem of general resonant systems is still remained open. The generalized Glimm scheme is introduced to establish the global existence results for some special 2 by 2 resonant systems.

NCTS(South)/ NCKU Math Colloquium

DATE	2014-02-27　16:10-17:00

PLACE	R204, 2F, NCTS, NCKU

SPEAKER	洪盟凱教授（中央大學數學系）

TITLE	Hyperbolic Resonant Systems of Balance Laws

ABSTRACT	In this talk we consider some 2 by 2 and 3 by 3 hyperbolic resonant systems of balance laws arise in fluid dynamics, traffic flows and solid mechanics. We say a system of conservation laws is resonant in some domain if the eigenvalues of Jacobian matrix of the flux coincide in this domain. The existence, uniqueness and properties of the entropy solutions to the Riemann problem is studied. A new entropy wave, which is called the composite elementary waves, is also introduced. The problem related to the global existence of weak solutions for the Cauchy problem of general resonant systems is still remained open. The generalized Glimm scheme is introduced to establish the global existence results for some special 2 by 2 resonant systems.