By Dan-Andrei Geba,Manoussos G Grillakis
The wave maps procedure is likely one of the most lovely and tough nonlinear hyperbolic structures, which has captured the eye of mathematicians for greater than thirty years now. within the learn of its a number of matters, reminiscent of the well-posedness concept, the formation of singularities, and the steadiness of the solitons, to be able to receive optimum effects, one has to exploit problematic instruments coming not just from research, but additionally from geometry and topology. furthermore, the wave maps process is not anything except the Euler–Lagrange procedure for the nonlinear sigma version, that is one of many basic difficulties in classical box theory.
One of the ambitions of our booklet is to provide an up to date and virtually self-contained assessment of the most regularity effects proved for wave maps.
Another one is to introduce, to a large mathematical viewers, bodily prompted generalizations of the wave maps approach (e.g., the Skyrme model), that are tremendous attention-grabbing and tough of their personal right.
Read or Download An Introduction to the Theory of Wave Maps and Related Geometric Problems PDF
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