Motivated by the paraxial narrow–angle approximation of the Helmholtz equation in domains of variable topography that appears as an important application in Underwater Acoustics, we analyze a general Schrödinger-type equation posed on two-dimensional variable domains with mixed boundary conditions. The resulting initialand boundary-value problem is transformed into an equivalent one posed on a ...

An inverse spectral problem is studied for second-order differential operators on hedgehog-type graphs with standard matching conditions in internal vertices and with mixed boundary conditions in boundary vertices. We prove a uniqueness theorem of recovering the coefficients of differential equations and boundary conditions from the given spectral characteristics. AMS Subject Classifications: A...

We consider the mixed boundary value problem for the Stokes and steady NavierStokes equations in two-dimensional domain with corner points on boundary, where the boundary conditions change their type. Our goal is to prove some regularity results near corner points, where the boundary conditions change.