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Lectures
Seminar information archive ～11/04｜Next seminar｜Future seminars 11/05～
2026/12/11
13:00-14:45 Room #123 (Graduate School of Math. Sci. Bldg.)
Intensive Lecture: Special Topics in Mathematical Sciences II (Six sessions on 11/06,13,20,27, 12/04,11)
Chun-Hsiung Hsia (National Taiwan University)
The mathematical analysis of the kinetic theory (ENGLISH)
Intensive Lecture: Special Topics in Mathematical Sciences II (Six sessions on 11/06,13,20,27, 12/04,11)
Chun-Hsiung Hsia (National Taiwan University)
The mathematical analysis of the kinetic theory (ENGLISH)
[ Abstract ]
The existence theory and the regularity theory are two important issues in the study of PDE problems. To establish the existence theory, one can resort to:
(1)the compactness of the solution operator to apply fixed point arguments or contraction mapping arguments
(2)the existence theory by functional analysis, for example: the Fredholm alternative, the method of continuity, semigroup theory, .. etc.
The regularity theory seems to be the next issue after one obtains the existence theory. In fact, the regularity can help to establish the compactness of solution operators, and therefore helps to establish the existence theory. In this course, we have shall reveal the aforementioned theory and apply this framework to investigate the Boltzmann equations.
The existence theory and the regularity theory are two important issues in the study of PDE problems. To establish the existence theory, one can resort to:
(1)the compactness of the solution operator to apply fixed point arguments or contraction mapping arguments
(2)the existence theory by functional analysis, for example: the Fredholm alternative, the method of continuity, semigroup theory, .. etc.
The regularity theory seems to be the next issue after one obtains the existence theory. In fact, the regularity can help to establish the compactness of solution operators, and therefore helps to establish the existence theory. In this course, we have shall reveal the aforementioned theory and apply this framework to investigate the Boltzmann equations.
