Sentence examples for propagation of singularities from inspiring English sources

We construct a modified propagator, and then by using this propagator and also the propagator of the unperturbed free harmonic oscillator we characterize the propagation of singularities for solutions to the equations.

If we are interested in the propagation of singularities without applications to spectral asymptotics, the answer is "singularities propagate along the generalized Hamiltonian billiards" (see Definition 3.2.2 in [14]).

Propagation of singularities.

1.2, albeit one needs to describe the propagation of singularities.

2.1.4, we can improve our asymptotics under certain conditions to the dynamics of propagation of singularities.

Semiclassical microlocal analysis, propagation of singularities and related dynamics play crucial role.

We revisit three problems on the propagation of conormal singularities for semilinear wave equations: the evolution of two simply tangent waves, the interaction of three conormal waves, and the evolution of one wave with a cusp singularity.

If the magnetic field is weak enough, we use the incomplete canonical form only to study propagation of the singularities and if the magnetic field is sufficiently strong, the omitted terms (O(mu ^{-4})) in the canonical form are small enough to be neglected.

As a result, the unsteady behavior of the solution, such as the propagation of discontinuities and some weaker singularities in the molecular velocity distribution function, are clarified.

One of the most remarkable features of singularities is their persistence.

The most problematic kinds of singularities, in terms of determinism, are naked singularities (singularities not hidden behind an event horizon).