Summer 2016

BMS-Course Infinite-Dimensional Dynamics of Global Attractors

Prof. Dr. Bernold Fiedler

Recitation session: Hannes Stuke

Schedule, Summer 2016

Lecture:

Tuesday, 10.15-14.00, seminar room 140, Arnimallee 7 (rear building)

Recitation session:

Monday, 12.00-14.00, seminar room 140, Arnimallee 7 (rear building)

Written examination:

Tuesday 19.07.2016, 10.15-11:45, seminar room 140, Arnimallee 7 (rear building)

Results: (PDF)

Resit:

Thursday 20.10.2016, 10.15-11:45, seminar room 140, Arnimallee 7 (rear building)

Topics

Thesis work will develop in class.

Prerequisites

Basic concepts of dynamical systems OR basic concepts of partial differential equation - and a fresh mind.

References

• H.-W. Alt: Lineare Funktionalanalysis. Springer, 1985.
• R. Courant and D. Hilbert: Methoden der Mathematischen Physik I, II. Springer, 1924.
• L.C. Evans: Partial Differential Equations. Graduate Studies in Mathematics. American Mathematical Society, 1998.
• A. Friedman: Partial Differential Equations of Parabolic Type. Prentice Hall, 1964.
• A. Friedman: Partial Differential Equations. Holt et al., 1969.
• D. Gilbarg and N.S. Trudinger: Elliptic Partial Differential Equations of Second Order. Springer, 1977.
• D. Henry: Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Math. 840. Springer, 1981.
• T. Kato: Perturbation Theory for Linear Operators. Springer, 1966.
• A. Pazy: Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer, 1983.
• H. Tanabe: Equations of Evolution. Pitman, 1979.
• E. Zeidler: Vorlesungen über nichtlineare Funktionalanalysis I-V. Teubner, 1980-1982. English translation by Springer, 1988-1993.

see for a general background:

• D. Henry: Geometric Theory of Semilinear Parabolic Equations, Lect. Notes Math. 840, Springer-Verlag, New York, 1981.
• A. Pazy: Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.
• H. Tanabe, Equations of Evolution, Pitman, Boston, 1979.

see for global attractors in general:

• A.V. Babin and M.I. Vishik: Attractors of Evolution Equations, North Holland, Amsterdam, 1992.
• V.V. Chepyzhov and M. I. Vishik: Attractors for Equations of Mathematical Physics, Colloq. AMS, Providence, 2002.
• A. Eden, C. Foias, B. Nicolaenko and R. Temam: Exponential Attractors for Dissipative Evolution Equations, Wiley, Chichester, 1994.
• J.K. Hale: Asymptotic Behavior of Dissipative Systems, Math. Surv., 25. AMS Publications, Providence, 1988.
• J.K. Hale, L. T. Magalhaes and W. M. Oliva, Dynamics in Infinite Dimensions, Springer- Verlag, New York, 2002.
• O.A. Ladyzhenskaya, Attractors for Semigroups and Evolution Equations, Cambridge University Press, 1991.
• G. Raugel, Global attractors in partial differential equations, Handbook of dynamical systems, 2 (2002), 885-982.
• G. R. Sell and Y. You: Dynamics of Evolutionary Equations, Springer-Verlag, New York, 2002.
• R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer- Verlag, New York, 1988.

see for functional differential equations:

• R. Bellman and K.L. Cooke: Differential-Difference Equations. Academic Press, New York,1963.
• O. Diekmann, S.A. van Gils, S. M. Verduyn-Lunel and H. O. Walther: Delay Equations: Functional-, Complex-, and Nonlinear Analysis, vol. 110. Springer, New York, 1995.
• J.K. Hale: Theory of Functional Differential Equations. Springer, New York, 1977.
• J.K. Hale and S.M. Verduyn-Lunel: Introduction to Functional Differential Equations. Springer, New York, 1993.
• V. Kolmanovski and A. Myshkis: Introduction to the Theory and Applications of Functional Differential Equations. Kluwer, Dordrecht, 1999.
• R.G. Nussbaum: Functional differential equations. In: B. Fiedler (ed.): Handbook of Dynamical Systems, vol. 2, pp. 461-499. Elsevier/North-Holland, Amsterdam, 2002.
• W. M. Oliva: Functional Differential Equations - Generic Theory. Dynamical Systems Vol. 1, 1977
• H.-O. Peitgen and H.-O. Walther: Functional Differential Equations and Approximation of Fixed Points. Lecture Notes in Mathematics, 1978.
• H. Smith: An Introduction to Delay Differential Equations with Applications to the Life Sciences. Tests in Applied Mathematics 57, 2011
• J. Wu: Theory and Applications of Partial Functional Differential Equations. Springer, New York, 1996.

Homework assignments, Summer 2016

1. Homework assignment, due May 03, 2016 (PDF)
2. Homework assignment, due May 10, 2016 (PDF)
3. Homework assignment, due May 17, 2016 (PDF)
4. Homework assignment, due May 24, 2016 (PDF)
5. Homework assignment, due May 31, 2016 (PDF)
6. Homework assignment, due June 07, 2016 (PDF)
7. Homework assignment, due June 14, 2016 (PDF)
8. Homework assignment, due June 21, 2016 (PDF)
9. Homework assignment, due June 28, 2016 (PDF)
10. Homework assignment, due July 05, 2016 (PDF)
11. Homework assignment, due July 12, 2016 (PDF)

Core questions, Summer 2016