# Basic tools for finite and infinite-dimensional systems, Lecture 3.

Tuesday, September 18, 2012 - 9:00am - 10:30am

Keller 3-180

Peter Bates (Michigan State University)

PDEs as conservative or dissipative systems. Stability and instability of solutions.

REFERENCES:

1. Dan Henry; Geometric Theory of Semilinear Parabolic Equations, Springer Lecture Notes 840. 2. Chapters 1 and 6 at least.

1. A. Pazy; Semigroups of Linear Operators and Applications to PDEs, Springer Applied Math 44, 2. Chapters 1, 2, and 4.

3. R. Temam; Infinite Dimensional Dynamical Systems in Mechanics and Physics, Springer Applied Math 68, Chapters 1-3.

4. P. Bates and C. Jones; Invariant Manifolds for Semilinear PDEs, Dynamics Reported V2, 1989.

5. K, Nakanishi and W. Schlag, Invariant Manifolds and Dispersive Hamiltonian Evolution Eqts, European Math Soc. 2011.

6. Unstable manifolds of Euler equations, Z. Lin and C. Zeng, â€¨avalaible at arxiv.org

7. Inviscid dynamical structures near Couette flow, Z. Lin and C. â€¨Zeng, ARMA and also avalaible at arxiv.org

8. Existence and persistence of invariant manifolds for semiflows in â€¨Banach space, P. Bates, K. Lu, and C. Zeng, Memoirs of AMS

9. Approximately invariant manifolds and global dynamics of spike â€¨states, P. Bates, K. Lu, and C. Zeng, Inventiones mathematicae

10. Invariant manifolds around soliton manifolds for the nonlinear ¨Klein-Gordon equation, Kenji Nakanishi, Wilhelm Schla, SIAM Math. Anal. and also avalaible at arxiv.org

REFERENCES:

1. Dan Henry; Geometric Theory of Semilinear Parabolic Equations, Springer Lecture Notes 840. 2. Chapters 1 and 6 at least.

1. A. Pazy; Semigroups of Linear Operators and Applications to PDEs, Springer Applied Math 44, 2. Chapters 1, 2, and 4.

3. R. Temam; Infinite Dimensional Dynamical Systems in Mechanics and Physics, Springer Applied Math 68, Chapters 1-3.

4. P. Bates and C. Jones; Invariant Manifolds for Semilinear PDEs, Dynamics Reported V2, 1989.

5. K, Nakanishi and W. Schlag, Invariant Manifolds and Dispersive Hamiltonian Evolution Eqts, European Math Soc. 2011.

6. Unstable manifolds of Euler equations, Z. Lin and C. Zeng, â€¨avalaible at arxiv.org

7. Inviscid dynamical structures near Couette flow, Z. Lin and C. â€¨Zeng, ARMA and also avalaible at arxiv.org

8. Existence and persistence of invariant manifolds for semiflows in â€¨Banach space, P. Bates, K. Lu, and C. Zeng, Memoirs of AMS

9. Approximately invariant manifolds and global dynamics of spike â€¨states, P. Bates, K. Lu, and C. Zeng, Inventiones mathematicae

10. Invariant manifolds around soliton manifolds for the nonlinear ¨Klein-Gordon equation, Kenji Nakanishi, Wilhelm Schla, SIAM Math. Anal. and also avalaible at arxiv.org

MSC Code:

37Lxx

Keywords: