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.
Sine - Laplace Equation, Sinh-Laplace Equation and Harmonic Maps.
Single input controllability of a simplified fluid-structure interaction model
In this paper we study a controllability problem for a simplified one dimensional model for the motion of a rigid body in a viscous fluid. The control variable is the velocity of the fluid at one end. One of the novelties brought in with respect to the existing literature consists in the fact that we use a single scalar control. Moreover, we introduce a new methodology, which can be used for other nonlinear parabolic systems, independently of the techniques previously used for the linearized problem....
Singular Asymptotic Expansions and Delta Waves for Burger's Equation.
Singular Convergence of Weak Solutions for a Quasilinear Nonhomogeneous.
Singular Perturbations for a Class of Degenerate Parabolic Equations with Mixed Dirichlet-Neumann Boundary Conditions
We establish a singular perturbation property for a class of quasilinear parabolic degenerate equations associated with a mixed Dirichlet-Neumann boundary condition in a bounded domain of , . In order to prove the -convergence of viscous solutions toward the entropy solution of the corresponding first-order hyperbolic problem, we refer to some properties of bounded sequences in together with a weak formulation of boundary conditions for scalar conservation laws.