The monograph is devoted to the study of initial-boundary-value problems for multi-dimensional Sobolev-type equations over bounded domains. The authors consider both specific initial-boundary-value problems and abstract Cauchy problems for first-order (in the time variable) diff…
This graduate-level, course-based text is devoted to the 3+1 formalism of general relativity, which also constitutes the theoretical foundations of numerical relativity. The book starts by establishing the mathematical background (differential geometry, hypersurfaces embedded in…
In multidimension, the Cauchy problem for a first order quadrilinear strictly hyperbolic system with a continuous data whose first derivatives are discontinuous on an hypersurface, is a free characteristic boundaries problem. We solve it locally in a blown-up configuration into …
