Some remarks on well-posedness of the higher-dimensional chemorepulsion system

• Autorzy: Cieślak Tomasz , Fujie Kentarou

Identyfikatory

DOI

10.4064/ba190324-4-6

• Języki publikacji: EN

Abstrakty

EN

We consider a fully parabolic system of chemorepulsion in higher dimensions. We introduce a new energy-like identity and comment on its relation to the Li-Yau-Hamilton inequalities. Next, we show that for the chemorepellent moving much more slowly than the cells, the time global well-posedness holds.

Słowa kluczowe

EN

boundedness of solutions; chemotaxis; Lyapunov-like functional

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2019
• Tom: Vol. 67, no. 2
• Strony: 165--178
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Cieślak Tomasz

• Institute of Mathematics, Polish Academy of Sciences, 00-656 Warszawa, Poland

autor

Fujie Kentarou

• Research Alliance Center for Mathematical Sciences, Tohoku University, Sendai, 980-8578, Japan

Bibliografia

• [1] D. Bakry, I. Gentil and M. Ledoux, Analysis and Geometry of Markov Diffusion Operators, Springer, 2014.
• [2] D. Bakry and M. Ledoux, A logarithmic Sobolev form of the Li-Yau parabolic inequality, Rev. Mat. Iberoamer. 22 (2006), 683-702.
• [3] D. Bothe, A. Fischer, M. Pierre and G. Rolland, Global existence for diffusion-electromigration systems in space dimension three and higher, Nonlinear Anal. 99 (2014), 152-166.
• [4] T. Cieślak, Ph. Laurençot and C. Morales-Rodrigo, Global existence and convergence to steady states in a chemorepulsion system, in: Parabolic and Navier-Stokes Equations, Banach Center Publ. 81, Inst. Math., Polish Acad. Sci., 2008, 105-117.
• [5] M. Freitag, Global existence and boundedness in a chemorepulsion system with superlinear diffusion, Discrete Contin. Dynam. Systems 38 (2018), 5943-5961.
• [6] K. Fujie and T. Senba, A sufficient condition of sensitivity functions for boundedness of solutions to a parabolic-parabolic chemotaxis system, Nonlinearity 31 (2018), 1639-1672.
• [7] K. Fujie and T. Senba, Application of an Adams type inequality to a two-chemical substances chemotaxis system, J. Differential Equations 263 (2017), 88-148.
• [8] R. Hamilton, A matrix Harnack estimate for the heat equation, Comm. Anal. Geom. 1 (1993), 113-126.
• [9] M. Hieber and J. Prüss, Heat kernels and maximal Lp-Lq estimates for parabolic evolution equations, Comm. Partial Differential Equations 22 (1997), 1647-1669.
• [10] P. Li and S.-T. Yau, On the parabolic kernel of the Schrödinger operator, Acta Math. 156 (1986), 153-201.
• [11] K. Lin and C. Mu, Global existence and convergence to steady states for an attractionrepulsion chemotaxis system, Nonlinear Anal. Real World Appl. 31 (2016), 630-642.
• [12] M. S. Mock, An initial value problem from semiconductor device theory, SIAM J. Math. Anal. 5 (1974), 597-612.
• [13] Y. Tao, Global dynamics in a higher-dimensional repulsion chemotaxis model with nonlinear sensitivity, Discrete Contin. Dynam. Systems Ser. B 18 (2013), 2705-2722.
• [14] Y. Tao and Z.-A. Wang, Competing effects of attraction vs. repulsion in chemotaxis, Math. Models Methods Appl. Sci. 23 (2013), 1-36.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).