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.
Singular perturbations for a class of quasi-linear hyperbolic equations
Singular solutions to Protter's problem for the 3-D wave equation involving lower order terms.
Singular solutions to systems of conservation laws and their algebraic aspects
We discuss the definitions of singular solutions (in the form of integral identities) to systems of conservation laws such as shocks, δ-, δ’-, and -shocks (n = 2,3,...). Using these definitions, the Rankine-Hugoniot conditions for δ- and δ’-shocks are derived. The weak asymptotics method for the solution of the Cauchy problems admitting δ- and δ’-shocks is briefly described. The algebraic aspects of such singular solutions are studied. Namely, explicit formulas for flux-functions of singular solutions...
Singularités des solutions d'équations d'ondes semi-linéaires
Singularities of the scattering kernel for generic obstacles
Singularities of the scattering kernel for non convex obstacles
Singularities of the scattering kernel for trapping obstacles
Singularity formation in systems of non-strictly hyperbolic equations.
Singularly perturbed hyperbolic problems on metric graphs: asymptotics of solutions
We are interested in the evolution phenomena on star-like networks composed of several branches which vary considerably in physical properties. The initial boundary value problem for singularly perturbed hyperbolic differential equation on a metric graph is studied. The hyperbolic equation becomes degenerate on a part of the graph as a small parameter goes to zero. In addition, the rates of degeneration may differ in different edges of the graph. Using the boundary layer method the complete asymptotic...
Singularly perturbed telegraph equations with applications in the random walk theory.
Sistemi iperbolici di leggi di conservazione
This survey paper provides a brief introduction to the mathematical theory of hyperbolic systems of conservation laws in one space dimension. After reviewing some basic concepts, we describe the fundamental theorem of Glimm on the global existence of BV solutions. We then outline the more recent results on uniqueness and stability of entropy weak solutions. Finally, some major open problems and research directions are discussed in the last section.
Slepian's inequality and commuting semigroups
Small analytic solutions to nonlinear weakly hyperbolic systems
Small data scattering for nonlinear Schrödinger wave and Klein-Gordon equations
Small data scattering for nonlinear Schrödinger equations (NLS), nonlinear wave equations (NLW), nonlinear Klein-Gordon equations (NLKG) with power type nonlinearities is studied in the scheme of Sobolev spaces on the whole space with order . The assumptions on the nonlinearities are described in terms of power behavior at zero and at infinity such as for NLS and NLKG, and for NLW.
Small solutions to semi-linear wave equations with radial data of critical regularity.