Abstract We consider a singular limit problem of the Cauchy for Patlak–Keller–Segel equation in scaling critical function space. It is shown that solution to system space involving class bounded mean oscillations converges drift-diffusion parabolic-elliptic type (simplified Keller–Segel model) strongly as relaxation time parameter $$\tau \rightarrow \infty $$ <mml:math xmlns:mml="http://www.w3....

We address a Cauchy problem for a nonlinear elliptic PDE arising in glaciology. After recasting the Cauchy problem as an ill-posed operator equation, we prove (for values of a certain parameter allowing Hilbert space techniques) differentiability properties of the associated operator. We also suggest iterative methods which can be applied to solve the operator problem.

Median problem for an arbitrary complex of abstract cubes is studied. First, a number of auxiliary results related to some special metric properties of abstract n-dimensional cube are presented. Basing on these results and results obtained in the study of homogeneous complexes [13], it is proved that median of an arbitrary complex of abstract cubes can be calculated without using metrics. Metho...