Measure Differential Equations (MDE): Absolutely Continuous (ac) Measures vs Completely Singular (cs) Measures-数学中心
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Measure Differential Equations (MDE): Absolutely Continuous (ac) Measures vs Completely Singular (cs) Measures

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Title: Measure Differential Equations (MDE): Absolutely Continuous (ac) Measures vs Completely Singular (cs) MeasuresSpeaker: Meirong Zhang (清华大学)Time: 16:00 - 17:00, July 15, 2018Location: Center for Mathematical Sciences, Room 813Abstract:  Measure Differential Equations (MDE) can be considered as the limiting case of the usual Differential Equations. In this talk, by taking the spatial ...

Title: Measure Differential Equations (MDE): Absolutely Continuous (ac) Measures vs Completely Singular (cs) Measures

Speaker: Meirong Zhang (清华大学)

Time: 16:00 - 17:00, July 15, 2018

Location: Center for Mathematical Sciences, Room 813

Abstract:  

Measure Differential Equations (MDE) can be considered as the limiting case of the usual Differential Equations. In this talk, by taking the spatial oscillation of 1D strings with general distributions of masses as an example, we will discuss how solutions and eigenvalues of MDE depend on measures in MDE. As a consequence of the so-called completely continuous dependence, we will show that ODEs and Algebraic Equations (AEs) can be mutually approximated, including their solutions, eigenvalues, etc. These results may be used to solve some applied problems, and even to yield some numerical methods for finding eigenvalues.