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Science/Engineering Semilinear Schrodinger Equations
Posted on 2010-03-15
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More Semilinear Schrodinger Equations (Courant Lecture Notes): Thierry Cazenave The nonlinear Schr& xF6;dinger 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 Korteweg-de Vries equation. From the mathematical point of view, Schr& xF6;dinger's equation is a delicate problem, possessing a mixture of the properties of parabolic and elliptic equations. Useful tools in studying the nonlinear Schr& xF6;dinger equation are energy and Strichartz's estimates. This book presents various mathematical aspects of the nonlinear Schr& xF6;dinger equation. It studies both problems of local nature (local existence of solutions, uniqueness, regularity, smoothing effect) and problems of global nature (finite-time 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 self-contained. Password: posted_by_mephistopheles96
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