By Dan-Andrei Geba,Manoussos G Grillakis
The wave maps approach is likely one of the most pretty and hard nonlinear hyperbolic platforms, which has captured the eye of mathematicians for greater than thirty years now. within the learn of its numerous concerns, equivalent to the well-posedness idea, the formation of singularities, and the steadiness of the solitons, for you to receive optimum effects, one has to take advantage of difficult instruments coming not just from research, but in addition from geometry and topology. furthermore, the wave maps approach is not anything except the Euler–Lagrange process for the nonlinear sigma version, that's one of many basic difficulties in classical box theory.
One of the pursuits of our e-book is to offer an updated and nearly self-contained evaluate of the most regularity effects proved for wave maps.
Another one is to introduce, to a large mathematical viewers, bodily influenced generalizations of the wave maps process (e.g., the Skyrme model), that are tremendous fascinating and hard of their personal right.
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Extra info for An Introduction to the Theory of Wave Maps and Related Geometric Problems