Propagation of singularities for hyperbolic operators with constant coefficient principal part

A Linear First-order Hyperbolic Equation with a Discontinuous Coefficient: Distributional Shadows and Propagation of Singularities

It is well-known that distributional solutions to the Cauchy problem for ut +(b(t, x)u)x = 0 with b(t, x) = 2H(x− t), where H is the Heaviside function, are non-unique. However, it has a unique generalized solution in the sense of Colombeau. The relationship between its generalized solutions and distributional solutions is established. Moreover, the propagation of singularities is studied.

Moduli Spaces of Semiquasihomogeneous Singularities with Fixed Principal Part

Real Hypersurfaces with Constant Principal Curvatures in Complex Hyperbolic Spaces

We present the classification of all real hypersurfaces in complex hyperbolic space CHn, n ≥ 3, with three distinct constant principal curvatures.

Propagation of Singularities and Growth for Schrödinger Operators

Spectral Analysis for Differential Operators with Singularities

Nonselfadjoint boundary value problems for second-order differential equations on a finite interval with nonintegrable singularities inside the interval are considered under additional sewing conditions for solutions at the singular point. We study properties of the spectrum, prove the completeness of eigenand associated functions, and investigate the inverse problem of recovering the boundary ...