Semilinear schrodinger equations thierry cazenave download. Cazenave, semilinear schrodinger equations, courant lecture notes in mathematics, new york university, 2003. Semilinear schrodinger equations pdf free download epdf. Thierry cazenave and alain haraux translated by yvan martel. Enter your mobile number or email address below and well send you a link to download the free kindle app. An introduction to semilinear elliptic equations thierry cazenave laboratoire jacqueslouis lions umr cnrs 7598 b. Newtons laws, the schrodinger equation does not give the trajectory of a particle, but rather the wave function of the quantum system, which carries information about the wave nature of the particle, which allows us to only discuss the probability of nding the. Request pdf on jan 1, 2003, thierry cazenave and others published semilinear schrodinger equation find, read and cite all the research you need on researchgate. Then, in terms of the hamiltonian invariants, we derive a new sharp energy criterion for global existence and blowing up of solutions of the equation. Partial di erential equations nonlinear dispersive. A note on berestyckicazenaves classical instability.

Semilinear schrodinger equations courant lecture notes by thierry cazenave and a great selection of related books, art and collectibles available now at. For the rest of the paper, we focus on the study of finitetime radial blowup solutions, and prove a result on the concentration of the. The matrix nonlinear schrodinger equation in dimension 2. Semilinear schrodinger equations thierry cazenave download bok. Nonregularity in h\ older and sobolev spaces of solutions to the. In this paper we study the cauchy problem for the semilinear heat and schrodinger equations, with the nonlinear term. Download fullsize image the plan of the paper is as follows. In this paper we study the cauchy problem for the semilinear heat and schr odinger equations, with the nonlinear term fu juju. Weissler example, in dimension n 1, if u0x xin a neighborhood of 0, then the resulting solution wt,x of 1. It is said that the maximal time interval of existence of the solution blows up in a finite time when this time is finite, and the solution develops a singularity in a finite time. By using the tools developed by merle and raphael, we prove the existence of blowup phenomena in the energy space h 1. Several anomalies are highlighted and resolutions proposed. 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.

We discuss when a minimizing sequence with respect to e. New york university, courant institute of mathematical sciences, new york. Motivated by this work, ferreiravillamizarroasilva pams 09 studied 1 with 0 in such type of. Find all the books, read about the author, and more. As h 0, these states concentrate near critical points of the potential. We will indicate possible extensions and references. It is also a good model dispersive equation, since it is often technically simpler than other dispersive equations, such as the wave or kortewegde vries equation. Journal of mathematical analysis and applications, vol. Cazenave, semilinear schrodinger equations, courant lecture notes in mathematics, new. The nonlinear schrodinger equation has received a great deal of attention from mathematicians, in particular because of its applications to nonlinear optics.

We establish two types of new invariant evolution flows. Blowup of solutions to cubic nonlinear schrodinger equations with defect. Inhomogeneous equations and abstract semilinear problems 50 4. Request pdf on jan 1, 2003, thierry cazenave and others published semilinear schrodinger equation find, read and cite all the research you need on. An introduction to semilinear evolution please copy and paste this embed script to where you want to embed. Thierry cazenave universite pierre et marie curie 10 semilinear schrodinger equations courant institute of mathematical sciences new york university new york, new york american mathematical society providence, rhode island. Then you can start reading kindle books on your smartphone, tablet, or. Equations schrodinger equation with a cubic nonlinearity 1. Matsumuraon the asymptotic behavior of solutions of semilinear wave equations. This is the second semester of a year long course which serves as an introduction to the modern mathematical treatment of linear and nonlinear partial di erential equations. For dispersive equations, this type of space was rst employed by cazenave weissler math z. Stability of groundstates for a system of m coupled semilinear. A co publication of the ams and the courant institute.

Schrodinger schrodinger equation with a cubic nonlinearity. This condition is in terms of an exact stationary solution of a semilinear elliptic. Stability solution of the nonlinear schrodinger equation. From the mathematical point of view, schrodingers equation is a delicate problem, possessing a mixture of the properties of parabolic and elliptic equations. Semilinear schrodinger equations courant lecture notes in. Multipeak periodic semiclassical states for a class of. Gigasolutions for semilinear parabolic equations in lp and regularity of weak. An introduction to nonlinear schrodinger equations thierry cazenave. Oxford lecture series in mathematics and its applications. The cauchy problem for the critical nonlinear schrodinger equation. Communications in partial differential equations, vol. Global existence of small analytic solutions to schrodinger equations with quadratic nonlinearity. Sharp thresholds of global existence and blowup for a.

The nonlinear schrodinger equation with a quadratic potential. Semilinear schrodinger equation request pdf researchgate. Local wellposedness and blowup phenomena for a generalized camassaholm equation with peakon solutions. For a class of nonlinear schrodinger equations, we prove the existence of semiclassical stationary states with possibly infinitely many concentration points. Page personnelle thierry cazenave sorbonneuniversite. This volume represents a broad survey of current research in the fields of nonlinear analysis and nonlinear differential equations. Finite speed of disturbance for the nonlinear schrodinger equation. Multibump solutions for a strongly indefinite semilinear. An introduction to semilinear evolution equations, oxford lecture series in mathematics and its applications, oxford university press, oxford, 1998.

Schrodinger equation with a cubic nonlinearity eqworld. Finite speed of disturbance for the nonlinear schrodinger equation volume 149 issue 6 simao correia. This book presents in a selfcontained form the typical basic properties of solutions to semilinear evolutionary partial. Know that ebook versions of most of our titles are still available and may be downloaded. Thierry cazenave author visit amazons thierry cazenave page.

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