Fuchsian Reduction: Applications to Geometry, Cosmology and Mathematical Physics (Google eBoek)
Springer Science & Business Media, 14 sep. 2007 - 304 pagina's
Fuchsian reduction is a method for representing solutions of nonlinear PDEs near singularities. The technique has multiple applications including soliton theory, Einstein's equations and cosmology, stellar models, laser collapse, conformal geometry and combustion. Developed in the 1990s for semilinear wave equations, Fuchsian reduction research has grown in response to those problems in pure and applied mathematics where numerical computations fail. This work unfolds systematically in four parts, interweaving theory and applications. The case studies examined in Part III illustrate the impact of reduction techniques, and may serve as prototypes for future new applications. In the same spirit, most chapters include a problem section. Background results and solutions to selected problems close the volume. This book can be used as a text in graduate courses in pure or applied analysis, or as a resource for researchers working with singularities in geometry and mathematical physics.
Wat mensen zeggen - Een recensie schrijven
We hebben geen recensies gevonden op de gebruikelijke plaatsen.
analytic apply arbitrary functions argument assume assumptions asymptotics behavior blowup surface boundary bounded Cauchy data Cauchy problem Chap coefficients completes the proof components compute consider constant converges coordinates corresponding deﬁne defined deﬁnition denote derivatives determined detonation domain eigenvalues elliptic estimate expansion ﬁnd ﬁrst follows formal solutions Fuchsian equation Fuchsian PDEs Fuchsian singularity Fuchsian system Gowdy hyperbolic inequality integral inverse inverse function theorem Kichenassamy Lax pair leading Lemma linear Liouville equation Math matrix mean curvature metric monomials nonlinear wave nonlinear wave equations nonnegative norm obtain operator parameters partition of unity PNLDE polynomial proof of Theorem properties prove radius regularity Remark renormalized renormalized unknown resonance satisﬁes satisfy second reduction Sect singular solutions singularity data smooth Sobolev spaces solves space space-time theory vanishes variables wave equations write
Pagina 280 - G. Fibich, V. Malkin, G. Papanicolaou, "Beam self-focusing in the presence of small normal time dispersion", Phys.