This course gives a lecture on the theory of semigroups for linear operators and its application to partial differential equations. Theory of semigroups for linear operators are firstly explained; then as an application of the semigroup theory, partial differential equations of evolution type is considered. This course will be completed with "Advanced topics in Analysis F" in the next quarter.
The aim of this course is to learn some aspects of functional analytic method for partial differential equations through applications of the semigroup theory.
・To understand theory of semigroups for linear operators.
・To understand applications of the semigroup theory to partial differential equations.
linear operator, semigroup, resolvent, spectrum, evolution equation, partial differential equation
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||Practical and/or problem-solving skills|
This is a standard lecture course. There will be some assignments.
|Course schedule||Required learning|
|Class 1||The following topics will be covered in this order : -- Uniformly continuous semigroup -- Strongly continuous semigroup -- Hille-Yosida's Theorem -- Asymptotic behavior of semigroups -- Applications to partial differential equations||Details will be provided in class.|
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Details will be provided during each class.
Attendance and Assignments.
Basics of complex function theory, Lebesgue integral theory, functional analysis, and theory of ordinary differential equations