Semilinear diffraction of conormal waves (joint work with Melrose and Sa Barreto)
Semilinear geometric optics for generalized solutions.
Semilinear hyperbolic functional equations
We consider second order semilinear hyperbolic functional differential equations where the lower order terms contain functional dependence on the unknown function. Existence and uniqueness of solutions for t ∈ (0,T), existence for t ∈ (0,∞) and some qualitative properties of the solutions in (0,∞) are shown.
Semilinear Hyperbolic Systems and Equations with Singular Initial Data.
Semilinear hyperbolic systems in one space dimension with strongly singular initial data.
Semilinear wave equation on manifolds
Semilinear wave equations with angularly smooth data
Semilinear waves with cusp singularities
Sensors and boundary state reconstruction of hyperbolic systems
This paper deals with the problem of regional observability of hyperbolic systems in the case where the subregion of interest is a boundary part of the system evolution domain. We give a definition and establish characterizations in connection with the sensor structure. Then we show that it is possible to reconstruct the system state on a subregion of the boundary. The developed approach, based on the Hilbert uniqueness method (Lions, 1988), leads to a reconstruction algorithm. The obtained results...
Sets of removable singularities of an equation
Sharp condition for global existence and blow-up on Klein-Gordon equation.
Sharp Domains of Determinacy and Hamilton-Jacobi Equations
If is a linear hyperbolic system of partial differential operators for which local uniqueness in the Cauchy problem at spacelike hypersurfaces is known, we find nearly optimal domains of determinacy of open sets . The frozen constant coefficient operators determine local convex propagation cones, . Influence curves are curves whose tangent always lies in these cones. We prove that the set of points which cannot be reached by influence curves beginning in the exterior of is a domain of...
Sharp stability estimates for hyperbolic conservation laws.
Sharp regularity theory for second order hyperbolic equations of Neumann type
This note provides sharp regularity results for general, time-independent, second order, hyperbolic equations with non-homogeneous data of Neumann type.
Shock fluctuations in a particle system
Shock waves in gas dynamics.
Short-time Asymptotics of the two-Dimensional wave Equation for an Annular Vibrating Membrane with Piecewise smooth Boundary Conditions
Simultaneous controllability in sharp time for two elastic strings
We study the simultaneously reachable subspace for two strings controlled from a common endpoint. We give necessary and sufficient conditions for simultaneous spectral and approximate controllability. Moreover we prove the lack of simultaneous exact controllability and we study the space of simultaneously reachable states as a function of the position of the joint. For each type of controllability result we give the sharp controllability time.
Simultaneous controllability in sharp time for two elastic strings
We study the simultaneously reachable subspace for two strings controlled from a common endpoint. We give necessary and sufficient conditions for simultaneous spectral and approximate controllability. Moreover we prove the lack of simultaneous exact controllability and we study the space of simultaneously reachable states as a function of the position of the joint. For each type of controllability result we give the sharp controllability time.
Simultaneous exact controllability for Maxwell equations and for a second-order hyperbolic system.