Local existence of a solution of a semi-linear wave equation in a neighborhood of initial characteristic hypersurfaces

Abstract: We consider the semilinear wave equation with power nonlinearity in one space dimension. Given a blow-up solution with a characteristic point, we refine the blow-up

This paper is concerned with the existence and the regularity of global solutions to the linear wave equation associated the boundary conditions of two-point type.. We also

In 1994, they also considered submanifolds of a Riemannian manifold and obtained the equations of Gauss, Codazzi and Ricci associated with a semi-symmetric non-metric connection

Isolatedness of characteristic points at blow-up for a semilinear wave equation in one space dimension.. Frank Merle,

Existence and classification of characteristic points at blow-up for a semilinear wave equation in one space dimension. Determination of the curvature of the blow-up set and

Recently, Gazzola and Squassina [14] studied the global solution and the finite time blow-up for a damped semilinear wave equations with Dirichlet boundary conditions by a careful

The proof of this result (given in Appendix B), is based in a crucial way on the existence and uniqueness of the stable manifold.. The trajectories of X c E cross in a regular way

Croce: The regularizing effects of some lower order terms in an elliptic equation with degenerate coercivity. – Laboratoire de Math´ ematiques Appliqu´ ees du Havre, Univer- sit´ e