Preface; Notation; 1. Preliminaries and tools; 2. Linear dispersive equations; 3. Methods for establishing wellposedness; 4. Global dynamics of nonlinear dispersive PDEs; 5. Applications of smoothing estimates; References; Index.
Introduces nonlinear dispersive partial differential equations in a detailed yet elementary way without compromising the depth and richness of the subject.
M. Burak Erdoğan is a professor in the Department of Mathematics at the University of Illinois, Urbana-Champaign. Nikolaos Tzirakis is an associate professor in the Department of Mathematics at the University of Illinois, Urbana-Champaign.
'The exercises in each chapter, while not at all trivial,
tremendously enhance one's understanding of the material. The focus
on periodic boundary conditions sets this book apart from related
ones in the area, and yet the authors do a nice job discussing
related well-posedness results and estimates on the real line as
well. While certainly not meant for students without any analysis
background, a thorough work-through of this book certainly brings
one to the frontier of the theory of nonlinear dispersive PDEs.'
Eric Stachura, MAA Reviews
'The book is a manual for beginning graduate students in the field
of the general theory of nonlinear partial differential equations.
The material is presented in the rigorous mathematical style,
providing proofs of formal theorems, rather than less strict
considerations which may be often encountered in physics
literature.' Boris A. Malomed, Zentralblatt MATH
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