Singularities of the scattering kernel for trapping obstacles
Singularities of wave fronts at the boundary between two media
Singularity analysis and integrability of a Burgers-type system of Foursov.
Singularity and regularity -- local and global.
Singularity formation in systems of non-strictly hyperbolic equations.
Singularity of parabolic measures
Singularity patterns in a chemotaxis model.
Singularity theory and the geometry of a nonlinear elliptic equation
Singularly perturbed elliptic equations with solutions concentrating on a 1-dimensional orbit
We consider a singularly perturbed elliptic equation with superlinear nonlinearity on an annulus in , and look for solutions which are invariant under a fixed point free 1-parameter group action. We show that this problem can be reduced to a nonhomogeneous equation on a related annulus in dimension 3. The ground state solutions of this equation are single peak solutions which concentrate near the inner boundary. Transforming back, these solutions produce a family of solutions which concentrate...
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 periodic parabolic equations with alternating boundary layer type solutions.
Singularly perturbed set of periodic functional-differential equations arising in optimal control theory
We consider the singularly perturbed set of periodic functional-differential matrix Riccati equations, associated with a periodic linear-quadratic optimal control problem for a singularly perturbed delay system. The delay is small of order of a small positive multiplier for a part of the derivatives in the system. A zero-order asymptotic solution to this set of Riccati equations is constructed and justified.
Singularly perturbed telegraph equations with applications in the random walk theory.
Sistemi del tipo non globalmente risolubili
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.
Ski de fond
Skipping transition conditions in a posteriori error estimates for finite element discretizations of parabolic equations
In this paper we derive a posteriori error estimates for the heat equation. The time discretization strategy is based on a θ-method and the mesh used for each time-slab is independent of the mesh used for the previous time-slab. The novelty of this paper is an upper bound for the error caused by the coarsening of the mesh used for computing the solution in the previous time-slab. The technique applied for deriving this upper bound is independent of the problem and can be generalized to other time...
Slepian's inequality and commuting semigroups
Slopes of hypergeometric systems of codimension one.
We describe the slopes, with respect to the coordinates hyperplanes, of the hypergeometric systems of codimension one, that is when the toric ideal is generated by one element.
Slowly oscillating solutions of a parabolic inverse problem: boundary value problems.