A5087222999- advanced mathematical theories
- Mathematical Biology Tumor Growth
- Advanced Mathematical Modeling in Engineering
- Fluid Dynamics and Turbulent Flows
- Stochastic processes and financial applications
- Advanced Topology and Set Theory
- Advanced Thermodynamics and Statistical Mechanics
- Topological and Geometric Data Analysis
- Nonlinear Partial Differential Equations
- Differential Equations and Boundary Problems
- Mathematical Dynamics and Fractals
- Homotopy and Cohomology in Algebraic Topology
- Gene Regulatory Network Analysis
- Genetics, Bioinformatics, and Biomedical Research
- Navier-Stokes equation solutions
- Geometric Analysis and Curvature Flows
- Statistical Mechanics and Entropy
- Numerical methods in inverse problems
- Functional Equations Stability Results
- Reservoir Engineering and Simulation Methods
- Sustainability in Higher Education
- University-Industry-Government Innovation Models
- Iterative Methods for Nonlinear Equations
- Interdisciplinary Research and Collaboration
- Genome Rearrangement Algorithms
Institute of Mathematics
2012-2024
National Academy of Sciences of Ukraine
2018-2024
Kyiv Academic University
2023
American University Kyiv
2023
Ukrainian-American Concordia University
2023
Nicolaus Copernicus University
2018
In a recent paper, K.Keller has given characterization of the Kolmogorov-Sinai entropy discrete-time measure-preserving dynamical system on base an increasing sequence special partitions. These partitions are constructed from order relations obtained via real-valued random vector, which can be interpreted as collection observables and is assumed to separate points it. present paper we relax separation condition in generalize entropy, providing statement equivalence sigma-algebras. On its...
In earlier papers (A. N. Kochubei, Pacif. J. Math., 269 (2014), 355-369; Math. Anal. Appl.483 (2020), Article 123609), one of the authors developed a theory pseudo-differential equations for radial real-valued functions on non-Archimedean local field, with some features resembling those classical ordinary differential equations. Here we consider this kind, but weak degeneration. Under various assumptions, prove existence and uniqueness mild solutions, their global extensions regularity property.
We develop a theory of generalized solutions the nonlinear evolution equations for complex-valued functions real positive time variable and $p$-adic spatial variable, which can be seen as non-Archimedean counterparts fractional porous medium equation. In this case, we face problem that ball is simultaneously open closed, thus having an empty boundary. To address issue, use algebraic structure field numbers apply Pontryagin duality to construct appropriate Sobolev type spaces. prove existence...