arXiv subjects

Krzysztof Krawczyk

Publications and source records attributed to Krzysztof Krawczyk.

4 recordsLinked to original sources

arXiv2026

Uncountably many maximally consistent neighborhood complete congruential modal logics

We solve an open problem posed by Peter Fritz in \cite{Fritz} by proving that there are uncountably many C-Post complete congruential modal logics which are neighborhood complete. The method is algebraic: we construct an uncountable sequence of varieties of modal algebras which are minimal in the lattice of all subvarieties of modal algebras and are generated by a single complete and atomic modal algebra.

math.LO↗

arXiv2026

Concentration of mass of solutions to aggregation-diffusion equations

We consider the aggregation-diffusion equation in the whole space with a mildly singular interaction kernel K = K(x) which behaves like |x|^k near the origin for some k $\in$ (0, 2). This equation, supplemented with nonnegative, bounded, and integrable initial data, possesses a global-in-time solution. We prove that the family of nonnegative, radially symmetric solutions of this equation, all sharing the same initial datum, focuses around the origin over a common finite time interval as $ε$ ___ 0.

math.AP↗

arXiv2025

Maehara Interpolation in Extensions of R-mingle

We show that there are exactly five quasivarieties of Sugihara algebras with the amalgamation property, and that all of these have the relative congruence extension property. As a consequence, we obtain that the amalgamation property and transferable injections property coincide for arbitrary quasivarieties of Sugihara algebras. These results provide a complete description of arbitrary (not merely axiomatic) extensions of the logic R-mingle that have the Maehara interpolation property, and further demonstrates that the Robinson property and Maehara interpolation property coincide for arbitrary extensions of R-mingle. Further, we show that the question of whether a given finitely based extension of R-mingle has the Maehara interpolation property is decidable.

math.LO↗

arXiv2021

Stability of constant steady states of a chemotaxis model

The Cauchy problem for the parabolic--elliptic Keller--Segel system in the whole $n$-dimensional space is studied. For this model, every constant $A \in \mathbb{R}$ is a stationary solution. The main goal of this work is to show that $A < 1$ is a stable steady state while $A > 1$ is unstable. Uniformly local Lebesgue spaces are used in order to deal with solutions that do not decay at spatial variable on the unbounded domain.

math.AP↗