## One-dimensional direct and inverse problems for one system arising in a two-phase medium

A one-dimensional system of the Hopf-type equations is considered. Axial solutions to problems in the field of modeling two-fluid interactions are sought. A nonlinear system of ordinary differential equations is obtained. Direct and inverse problems for the obtained ODE are considered. A theorem on local solvability is proven.

## The scenario of a possible impact event of the Cretaceous-Paleogene boundary based on the "orbital" hypothesis

The studying the regions of global seismic belts, to which giant impact structures belong, confirms the hypothesis of the possible attachment to the Earth of its satellite at the Cretaceous-Paleogene boundary and the coincidence of these belts and structures to the routes of its tangent flight along the Med-Eocene position...

## Investigation of one dynamic system arising in a two-fluid medium

The Cauchy problem for a one-dimensional homogeneous system of the Hopf-type equations arising in a two-fluid medium is considered. It is believed that energy dissipation occurs only due to the friction coefficient (analogous to Darcy) and the Cauchy data are given in the form of a finite trigonometric Fourier series...

## Kolpanskoye Lake near St. Petersburg. Origin hypothesis

A hypothesis is formulated about the formation of Kolpanskoye Lake, located in the vicinity of the city of Gatchina (near St. Petersburg, Russia) as a result of a meteorite fall. An approximate calculation of meteorite characteristics was performed using the energy model of the meteorite/ground dynamic system and nonlinear programming...

## The development dynamics of the "Afro-Baikal" and the expanded "Indonesian" transregional seismolineaments based on the creepex analysis

A study to identify the spatio-temporal relationship between strong
*MS* ≥ 7 seismic shocks and the preceding moderate mid-depth seismicity has led
to the need to consider territories that go far beyond the area of preparation of
its individual foci. First, there are the areas along the global seismolineaments...

## One-dimensional dynamic inverse problem for a system of Hopf-type equations

A dynamic inverse problem for a one-dimensional system of the Hopf-type equations is considered. A theorem on local solvability in the class of functions
analytic in the variable *x* is proved.