PDE Dynamics

This book provides an overview of the myriad methods for applying dynamical systems techniques to PDEs and highlights the impact of PDE methods on dynamical systems. Also included are many nonlinear evolution equations, which have been benchmark models across the sciences, and examples and techniques to strengthen preparation for research. PDE Dynamics: An Introduction is intended for senior undergraduate students, beginning graduate students, and researchers in applied mathematics, theoretical physics, and adjacent disciplines. Structured as a textbook or seminar reference, it can be used in courses titled Dynamics of PDEs, PDEs 2, Dynamical Systems 2, Evolution Equations, or Infinite-Dimensional Dynamics.

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Christian Kuehn is Lichtenberg Professor for Multiscale and Stochastic Dynamics at Technical University of Munich and has worked at the Max Planck Institute for Physics of Complex Systems and Vienna University of Technology as a postdoctoral fellow. He has been an MFO Leibniz Fellow and an APART Fellow of the Austrian Academy of Sciences, and he is a recipient of the Richard von Mises Prize for his contributions to nonlinear dynamics. His research interests lie at the interface of differential equations, dynamical systems, and mathematical modelling, and his key goal is analyzing multiscale problems and the effect of noise/uncertainty in various classes of ordinary, partial, and stochastic differential equations as well as in adaptive networks.

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