Institute of Mathematics AS CR, v. v. i.

The Maths of Life and Death

Author: Kaslová Michaela
Publication venue: Union of Czech Mathematicians and Physicists
Publication date: 01/01/2023
Field of study

summary:Autor publikace, Christian (Kit) Yates, je absolventem Oxfordu: DPhil., téma práce Mathematical Biology a M.Sc. na téma Maths Modelling and Scientific computing. V současnosti působí na Univerzitě v Bath. Jeho zaměření publikací má jedno společné: bez matematiky se neobejdeme

Author
Publication venue: Union of Czech Mathematicians and Physicists
Publication date: 01/01/2023
Field of study

Large time behavior in a quasilinear parabolic-parabolic-elliptic attraction-repulsion chemotaxis system

Author: Chiyo Yutaro
Publication venue: Department of Mathematics, Faculty of Science of Masaryk University, Brno
Publication date: 01/01/2023
Field of study

summary:This paper deals with a quasilinear parabolic-parabolic-elliptic attraction-repulsion chemotaxis system. Boundedness, stabilization and blow-up in this system of the fully parabolic and parabolic-elliptic-elliptic versions have already been proved. The purpose of this paper is to derive boundedness and stabilization in the parabolic-parabolic-elliptic version

Stabilization in degenerate parabolic equations in divergence form and application to chemotaxis systems

Author: Ishida Sachiko
Yokota Tomomi
Publication venue: Department of Mathematics, Faculty of Science of Masaryk University, Brno
Publication date: 01/01/2023
Field of study

summary:This paper presents a stabilization result for weak solutions of degenerate parabolic equations in divergence form. More precisely, the result asserts that the global-in-time weak solution converges to the average of the initial data in some topology as time goes to infinity. It is also shown that the result can be applied to a degenerate parabolic-elliptic Keller-Segel system

Finite-time blow-up in a two-species chemotaxis-competition model with single production

Author: Mizukami Masaaki
Tanaka Yuya
Publication venue: Department of Mathematics, Faculty of Science of Masaryk University, Brno
Publication date: 01/01/2023
Field of study

summary:This paper is concerned with blow-up of solutions to a two-species chemotaxis-competition model with production from only one species. In previous papers there are a lot of studies on boundedness for a two-species chemotaxis-competition model with productions from both two species. On the other hand, finite-time blow-up was recently obtained under smallness conditions for competitive effects. Now, in the biological view, the production term seems to promote blow-up phenomena; this implies that the lack of the production term makes the solution likely to be bounded. Thus, it is expected that there exists a solution of the system with single production such that the species which does not produce the chemical substance remains bounded, whereas the other species blows up. The purpose of this paper is to prove that this conjecture is true

Stability with respect to domain of the low Mach number limit of compressible heat-conducting viscous fluid

Author: Wróblewska-Kamińska Aneta
Publication venue: Department of Mathematics, Faculty of Science of Masaryk University, Brno
Publication date: 01/01/2023
Field of study

summary:We investigate the asymptotic limit of solutions to the Navier-Stokes-Fourier system with the Mach number proportional to a small parameter

\varepsilon \rightarrow 0

, the Froude number proportional to

\sqrt{\varepsilon}

and when the fluid occupies large domain with spatial obstacle of rough surface varying when

\varepsilon\rightarrow 0

. The limit velocity field is solenoidal and satisfies the incompressible Oberbeck–Boussinesq approximation. Our studies are based on weak solutions approach and in order to pass to the limit in a convective term we apply the spectral analysis of the associated wave propagator (Neumann Laplacian) governing the motion of acoustic waves

An unconditionally stable finite element scheme for anisotropic curve shortening flow

Author: Deckelnick Klaus
Nürnberg Robert
Publication venue: Department of Mathematics, Faculty of Science of Masaryk University, Brno
Publication date: 01/01/2023
Field of study

summary:Based on a recent novel formulation of parametric anisotropic curve shortening flow, we analyse a fully discrete numerical method of this geometric evolution equation. The method uses piecewise linear finite elements in space and a backward Euler approximation in time. We establish existence and uniqueness of a discrete solution, as well as an unconditional stability property. Some numerical computations confirm the theoretical results and demonstrate the practicality of our method

Asymptotic behavior of small-data solutions to a Keller-Segel-Navier-Stokes system with indirect signal production

Author: Yang Lu
Liu Xi
Hou Zhibo
Publication venue: Matematický ústav AV ČR
Publication date: 01/01/2023
Field of study

summary:We consider the Keller-Segel-Navier-Stokes system

\begin{cases} n_t+{\bf u}\cdot \nabla n =\Delta n - \nabla \cdot (n\nabla v ),& x\in \Omega ,\ t>0,\\ v_t +{\bf u}\cdot \nabla v=\Delta v -v+w, &x\in \Omega ,\ t>0,\\ w_t+{\bf u}\cdot \nabla w=\Delta w -w+n, &x\in \Omega ,\ t>0,\\ {\bf {u}}_t + ({\bf {u}}\cdot \nabla ){\bf {u}} = \Delta {\bf {u}} + \nabla P + n\nabla \phi ,\ \nabla \cdot {\bf u}=0, &x\in \Omega ,\ t>0, \end{cases}

which is considered in bounded domain

\Omega \subset \mathbb {R}^N

(N \in \{2,3\})

with smooth boundary, where

\phi \in C^{1+\delta }(\overline \Omega )

with

\delta \in (0,1)

. We show that if the initial data

\|n_0\|_{L^{{N}/{2}}(\Omega )}

\|\nabla v_0\|_{L^N(\Omega )}

\|\nabla w_0\|_{L^N(\Omega )}

and

\|{\bf u}_0\|_{L^N(\Omega )}

is small enough, an associated initial-boundary value problem possesses a global classical solution which decays to the constant state

({\bar n}_0,{\bar n}_0,{\bar n}_0,0)

exponentially with

{\bar n}_0:=(1/|\Omega |)\int _{\Omega }n_0(x){\rm d}x

The factorization of the weighted Hardy space in terms of multilinear Calderón-Zygmund operators

Author: He Suixin
Tao Shuangping
Publication venue: Matematický ústav AV ČR
Publication date: 01/01/2023
Field of study

summary:We give a constructive proof of the factorization theorem for the weighted Hardy space in terms of multilinear Calderón-Zygmund operators. The result is also new even in the linear setting. As an application, we obtain the characterization of weighted BMO space via the weighted boundedness of commutators of the multilinear Calderón-Zygmund operators

Oscillatory properties of third-order semi-noncanonical nonlinear delay difference equations

Author: Ayyappan Govindasamy
Chatzarakis George E.
Kumar Thaniarasu
Thandapani Ethiraj
Publication venue: Matematický ústav AV ČR
Publication date: 01/01/2023
Field of study

summary:We study the oscillatory properties of the solutions of the third-order nonlinear semi-noncanonical delay difference equation

D_3y(n)+f(n)y^\beta (\sigma (n))=0,

where

D_3 y(n)=\Delta (b(n)\Delta (a(n)(\Delta y(n))^\alpha ))

is studied. The main idea is to transform the semi-noncanonical operator into canonical form. Then we obtain new oscillation theorems for the studied equation. Examples are provided to illustrate the importance of the main results

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