Hyperbolic Conservation Laws and Entropy Conditions
Hyperbolic Conservation Laws are
nonlinear partial differential equations (PDE) which play a central
role in the nonlinear PDE's theory and have numerous important
applications in science and technology.
In this final talk we derive estimates which imply uniqueness of weak solution satisfying Kruzhkov's entropy condition.
In this final talk we derive estimates which imply uniqueness of weak solution satisfying Kruzhkov's entropy condition.
Hyperbolic Conservation Laws and Entropy Conditions
Hyperbolic Conservation Laws are
nonlinear partial differential equations (PDE) which play a central
role in the nonlinear PDE's theory and have numerous important
applications in science and technology.
In the second talk we discuss a Kruzhkov's entropy condition and derive estimates which imply uniqueness of weak solution satisfying such entropy condition.
In the second talk we discuss a Kruzhkov's entropy condition and derive estimates which imply uniqueness of weak solution satisfying such entropy condition.
Department of Mathematics
Western Michigan University
Hyperbolic Conservation Laws and Entropy Conditions
Hyperbolic Conservation Laws are
nonlinear partial differential equations (PDE) which play a central
role in the nonlinear PDE's theory and have numerous important
applications in science and technology.
In this talk we provide an introduction in the basic theory of Hyperbolic Conservation Laws including elements of the classical theory due to Kruzhkov (Kruzhkov's entropy condition).
In this talk we provide an introduction in the basic theory of Hyperbolic Conservation Laws including elements of the classical theory due to Kruzhkov (Kruzhkov's entropy condition).
Markowitz portfolio, capital asset pricing model and convex analysis
Disclaimer: the views expressed in this talk may subject to the bias of many years of obssession with convex analysis and may not be objective.
Department of Mathematics
Western Michigan University
Update on the Calculus II Skills Test
The department has been giving calculus II
students a skills test on first semester calculus problems for several
years. In the fall of 2006 the exam was switched to a uniform computer
generated exam. This fall a trial, in one section, was run of a
completely on-line version of the exam. This spring semester the switch
will be made to running only the on-line version of the exam.
This talk will go over the makeup of the exam and demonstrate what the students actually see. There will then be a demonstration of the instructors role in the on-line exams. Teachers will be responsible for adding and removing students from their class as well as downloading their students' test scores.
This talk will go over the makeup of the exam and demonstrate what the students actually see. There will then be a demonstration of the instructors role in the on-line exams. Teachers will be responsible for adding and removing students from their class as well as downloading their students' test scores.
Department of Mathematics
Western Michigan University
Loewy Decomposition of Linear Differential Equations
In this talk, I will review
the results leading to "the Loewy decomposition of linear
differential equations" and consider few examples.
Department of Mathematics
Western Michigan University
A New Schur-like Form for Matrices under Unitary Congruence
(continuation of October 3 talk)
Department of Mathematics
Western Michigan University
A New Schur-like Form for Matrices under Unitary Congruence
Dr.Yuri S. Ledyaev
Department of Mathematics
Western Michigan University
Commutators of flows and fields (after Mauhart and Michor)
Department of Mathematics
Western Michigan University
Commutators of flows and fields (after Mauhart and Michor)
This is the last talk in this series in which we discussed a proof of a global approximate-controllability result for infinite-dimensional control systems. This proof is based on a generalization (due to M.Mauhart and P.Michor) of a classical formula expressing Lie brackets of vector fields in terms of appropriate commutators of flows for Banach spaces. In this talk we discuss a derivation of the Mauhart-Michor result.
Dr.Yuri S. Ledyaev
Department of Mathematics
Western Michigan University
Commutators of flows and fields (after Mauhart and Michor)
This is a continuation of the previous talk under the same title in which we discussed a proof of a global approximate-controllability result for infinite-dimensional control systems. This proof is based on a generalization (due to M.Mauhart and P.Michor) of a classical formula expressing Lie brackets of vector fields in terms of appropriate commutators of flows for Banach spaces. In this talk we discuss a derivation of the Mauhart-Michor result.
Department of Mathematics
Western Michigan University
Commutators of flows and fields (after Mauhart and Michor)
This is a continuation of the previous talk under the same title in which we discussed a proof of a global approximate-controllability result for infinite-dimensional control systems. This proof is based on a generalization (due to M.Mauhart and P.Michor) of a classical formula expressing Lie brackets of vector fields in terms of appropriate commutators of flows for Banach spaces. In this talk we discuss a derivation of the Mauhart-Michor result.
Dr.Yuri S. Ledyaev
Department of Mathematics
Western Michigan University
Commutators of flows and fields (after Mauhart and Michor)
We discuss a generalization (due to M.Mauhart and P.Michor) of a classical formula expressing Lie brackets of vector fields in terms of appropriate commutators of flows for Banach spaces. In the case of finite-dimensional spaces such results have found important applications in geometric control theory. We start with a brief survey of relevant controllability results.
Department of Mathematics
Western Michigan University
Commutators of flows and fields (after Mauhart and Michor)
We discuss a generalization (due to M.Mauhart and P.Michor) of a classical formula expressing Lie brackets of vector fields in terms of appropriate commutators of flows for Banach spaces. In the case of finite-dimensional spaces such results have found important applications in geometric control theory. We start with a brief survey of relevant controllability results.