arXiv subjects

Louokdom Tamto Paul Giscard

Publications and source records attributed to Louokdom Tamto Paul Giscard.

2 recordsLinked to original sources

arXiv2026

Semi-global solutions to the Goursat problem for second-order hyper-quasilinear hyperbolic systems with lineary dependent principal coefficients and applications to the vacuum Einstein equations

In this work, we significantly extend the results of D. Houpa, 2006 on the Goursat problem for second-order semi-linear hyperbolic systems to the broader framwork of second-order hyper-quasilinear hyperbolic systems of Goursat type, in which the coefficients of the second-order derivatives depend linearly on the unknown. By adapting techniques inspired by Y. Foures (Choquet)- Bruhat, Acta Mathematica, 1952. we show that in the Sobolev type spaces for the Goursat problem quasilinear hyperbolic of the second order considered, the solution exists and is defined in the vicinity of the meeting characteristic hypersurfaces which carry the initial data. As an application, in harmonic gauge, we derive a semi-global existence and uniqueness result for the vacuum Einstein equations.

math.AP↗

arXiv2026

Solution of second-order hyperbolic quasilinear systems with spatio-characteristic initial data in weighted Sobolev-type spaces under finite differentiability assumptions on the data

The aim of this work is to establish an existence and uniqueness solution for spatiocharacteristic second-order quasilinear hyperbolic problems in Sobolev type spaces with weights to clarify and complete the previous work done by H. Muller Zum Hagen and H.J. Seifert, Gen. Rel. and Gravit. 1977. We use this result in P. G. Louokdom tamto, PhD thesis ongoing, 2026 to establish a semi-global existence and uniqueness result for second-order quasilinear Goursat problems where the coefficients of the second derivatives depend linearly on the unknown in weighted Sobolev-type spaces, which we will apply to the harmonic gauge vacuum Einstein equations

math.AP↗