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Maria Shubina

Publications and source records attributed to Maria Shubina.

8 recordsLinked to original sources
arXiv2023

Some exact solutions of Friedmann cosmological equation

In this paper we present a number of examples of exact solutions for the Friedmann cosmological equation for metric $ F(R) $ gravity model. Emphasis was placed on the possibility of obtaining exact time dependences of the main cosmological physical quantities: scale factor, scalar curvature, Hubble rate and function $ F(R) $. For this purpose an ansatz was used to reduce the Friedmann equation to an ordinary differential equation for function $ F = F(H^{2})$. This made it possible to obtain a number of exact solutions, both already known and new.

gr-qc↗
arXiv2022

Exact analytical vacuum solutions of $ R^n $-gravity model depending on two variables

In this paper we consider the metric power-law $f(R)\sim R^n $-gravity model for the four-dimensional metric tensor depending on two coordinates. We obtain exact analytical vacuum solutions for different values of $ n $. These solutions contain both non-stationary configurations of the travelling wave type and stationary ones, in particular, depending on one radial variable.

gr-qc↗
arXiv2021

Exact solutions in two-dimensional metric $f(R)$-gravity

In this paper we consider the two-dimensional metric $f(R)$-gravity model for the metric tensor depending on two variable: time and one spacelike coordinate. We obtain exact analytical vacuum solutions for different forms of function $ f(R) $ which are solutions of cosmological type. These solutions are expressed in terms of arbitrary functions, which, under certain conditions, can be chosen as new variables.

gr-qc↗
arXiv2018

Exact traveling wave solutions of one-dimensional models of cancer invasion

In this paper we consider continuous mathematical models of tumour growth and invasion based on the model introduced by Chaplain and Lolas \cite{Chaplain&Lolas2006}, for the case of one space dimension. The models consist of a system of three coupled nonlinear reaction-diffusion-taxis partial differential equations describing the interactions between cancer cells, the matrix degrading enzyme and the tissue. For these models under certain conditions on the model parameters we obtain exact analytical solutions in terms of traveling wave variables. These solutions are smooth positive definite functions for some of which whose profiles agree with those obtained from numerical computations \cite{Chaplain&Lolas2006} for not very large time intervals.

q-bio.TO↗
arXiv2017

The system of two parabolic equations as an integrable system

In this paper we present a system of two nonlinear partial differential equations of the second order, depending on the time and one spatial coordinate. It can be written as a system of two Burgers equations, which allows one to immediately conclude that it is integrable. This system seems to be new, and its consideration can be of independent interest.

nlin.SI↗
arXiv2016

The 1D parabolic-parabolic Patlak-Keller-Segel model of chemotaxis: the particular integrable case and soliton solution

In this paper we investigate the one-dimensional parabolic-parabolic Patlak-Keller-Segel model of chemotaxis. For the case when the diffusion coefficient of chemical substance is equal to two, in terms of travelling wave variables the reduced system appears integrable and allows the analytical solution. We obtain the exact soliton solutions, one of which is exactly the one-soliton solution of the Korteweg-de Vries equation.

nlin.SI↗