The nonlinear Schrodinger equation has received a great deal of attention from mathematicians, particularly because of its applications to nonlinear optics. It is also a good model dispersive equation, since it is often technically simpler than other dispersive equations, such as the wave or the Kortewegde Vries equation. From the mathematical point of view, Schrodinger's equation is a delicate problem, possessing a mixture of the properties of parabolic and elliptic equations. Useful tools in studying the nonlinear Schrodinger equation are energy and Strichartz's estimates. This book presents various mathematical aspects of the nonlinear Schrodinger equation. It studies both problems of local nature (local existence of solutions, uniqueness, regularity, smoothing effect) and problems of global nature (finitetime blowup, global existence, asymptotic behavior of solutions). In principle, the methods presented apply to a large class of dispersive semilinear equations. The first chapter recalls basic notions of functional analysis (Fourier transform, Sobolev spaces, etc.). Otherwise, the book is mostly selfcontained. It is suitable for graduate students and research mathematicians interested in nonlinear partial differential equations and applications to mathematical physics.
About Thierry Cazenave
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Author  :  Thierry Cazenave 
Publisher  :  American Mathematical Society 
Data Published  :  15 September 2003 
ISBN  :  0821833995 
EAN  :  9780821833995 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  323 pages 
Age +  :  15 years 
Language  :  English 
Rating  : 
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