Tools and Problems in Partial Differential Equations - Zuily, Claude

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Résumé :
This textbook offers a unique learning-by-doing introduction to the modern theory of partial differential equations. Through 65 fully solved problems, the book offers readers a fast but in-depth introduction to the field, covering advanced topics in microlocal analysis, including pseudo- and para-differential calculus, and the key classical equations, such as the Laplace, Schr?dinger or Navier-Stokes equations. Essentially self-contained, the book begins with problems on the necessary tools from functional analysis, distributions, and the theory of functional spaces, and in each chapter the problems are preceded by a summary of the relevant results of the theory. Informed by the authors' extensive research experience and years of teaching, this book is for graduate students and researchers who wish to gain real working knowledge of the subject. ...

Biographie:
Thomas Alazard is a senior researcher at CNRS. For several years, he has taught partial differential equations, microlocal analysis and functional analysis at the Ecole Normale Sup?rieure and the Ecole Normale Sup?rieure Paris-Saclay. His research focuses on the applications of harmonic analysis and microlocal analysis to the study of nonlinear partial differential equations. Claude Zuily received his PhD from Universit? Paris-Sud (Orsay), where he was professor of mathematics until 2010. Currently emeritus professor at Universit? Paris-Saclay, he is the author of several books: Uniqueness and non uniqueness in the Cauchy problem (Birkh?user 1983), Probl?mes de distributions et d'?quations aux d?riv?es partielles (Hermann 1995 and Cassini 2010), Analyse pour l'agr?gation (with H. Queff?lec) (Dunod 1995), Distributions et ?quations aux d?riv?es partielles (Dunod 2002). His primary areas of research are linear and nonlinear partial differentialequations. ...

Sommaire:
Thomas Alazard is a senior researcher at CNRS. For several years, he has taught partial differential equations, microlocal analysis and functional analysis at the Ecole Normale Sup?rieure and the Ecole Normale Sup?rieure Paris-Saclay. His research focuses on the applications of harmonic analysis and microlocal analysis to the study of nonlinear partial differential equations. Claude Zuily received his PhD from Universit? Paris-Sud (Orsay), where he was professor of mathematics until 2010. Currently emeritus professor at Universit? Paris-Saclay, he is the author of several books: Uniqueness and non uniqueness in the Cauchy problem (Birkh?user 1983), Probl?mes de distributions et d'?quations aux d?riv?es partielles (Hermann 1995 and Cassini 2010), Analyse pour l'agr?gation (with H. Queff?lec) (Dunod 1995), Distributions et ?quations aux d?riv?es partielles (Dunod 2002). His primary areas of research are linear and nonlinear partial differentialequations. ...