ISEM30: Evolution equations governed by accretive operators

The 30th International Internet Seminar is entitled

Evolution equations governed by accretive operators

Short description: This year's internet seminar deals with (in general nonlinear) abstract Cauchy problems of the form u'+Au∋f on [0,T], u(0)=u_0, where A is an accretive operator on a Banach space X. Many partial differential equations in science can be rewritten abstractly in this way, and a theory for the abstract Cauchy problem allows to treat them in a unified way. The following topics will be treated:
- Accretive operators and subgradients
- Wellposedness of the abstract Cauchy problem: existence, uniqueness and continuous dependence of solutions on data (f and u_0)
- Approximation theory
- Qualitative theory: e.g. comparison principles, regularity of solutions, ...
The project phase and the final workshop will complement this course which can only be an introduction to the theory.

Virtual lecturer: Ralph Chill (TU Dresden)

The internet seminar is temporarily divided into three phases: 
- Lecture phase: October 2026 - February 2027
- Project phase: February 2027 - May 2027
- Final workshop: May 2027

Registration on OPAL for access to the lectures and a discussion forum. Registration is free.

Lecture phase: During the lecture phase, the "virtual lecturer" uploads a new chapter of lecture notes on OPAL each week. Each chapter consists of approximately 10 pages plus a collection of exercise problems. In addition to the lecture notes, there will be an asynchronous video lecture. The participants read the lecture notes, watch the videos (if they like, not necessary) and work on the exercise problems. While doing so, they discuss and collaborate in two different ways:

• Via the forum on OPAL, which has LaTeX support. 
• Via local groups, seminars or courses at the participants' universities. At many universities, the participating students or lecturers organize a local ISEM group that meets regularly to discuss the lectures and the exercise problems. 
  Each week, the virtual lecturers will ask the local group of one university to provide the solutions to the week's exercises written in LaTeX, such that they can be uploaded to the ISEM webpage.

Project phase: Students who are interested to get even more engaged after the lecture phase can apply to participate in the ISEM's project phase. The participants of the project phase will be split into international groups of 3-5 students coordinated by experienced mathematicians. Each group studies one specific topic in depth - usually by reading a research article about the topic and discussing it online. Each group prepares a presentation for the on-site workshop in the third and final phase of the ISEM. Thus, participating in the project phase implies a commitment to participate in person in the final workshop.

Workshop: The workshop takes place at Kloster Marienthal / Ostritz from 28 May to 1 June 2027.

The Internet Seminars: The "Internet Seminar on Evolution Equations" is an international mathematical event that is organized annually by different mathematicians. Each year's organizers choose a topic - usually closely related to evolution equations and/or operator theory - and design a course that consists of three phases: an online lecture phase, an online project phase and an on-site workshop. Students from all over the world participate in the event.