曲率控制细胞和组织生长演化模型的Cauchy问题

数学物理学报 ›› 2023, Vol. 43 ›› Issue (3): 771-784.

曲率控制细胞和组织生长演化模型的Cauchy问题

王增桂()

聊城大学数学科学学院山东聊城 252059

收稿日期:2022-03-22 修回日期:2023-01-12 出版日期:2023-06-26 发布日期:2023-06-01
通讯作者: 王增桂 E-mail:wangzenggui@lcu.edu.cn
基金资助:
山东省自然科学基金(ZR2021MA084);聊城大学科研基金(318012025);聊城大学强特色智能科学与技术学科基金(319462208)

Cauchy Problem for the Evolution of Cells and Tissue During Curvature-Controlled Growth

Wang Zenggui()

School of Mathematical Sciences, Liaocheng University, Shandong Liaocheng 252059

Received:2022-03-22 Revised:2023-01-12 Online:2023-06-26 Published:2023-06-01
Contact: Zenggui Wang E-mail:wangzenggui@lcu.edu.cn
Supported by:
Natural Science Foundation of Shandong Province(ZR2021MA084);Scientific Research Foundation of Liaocheng University(318012025);Discipline with Strong Characteristics of Liaocheng University-Intelligent Science and Technology(319462208)

摘要/Abstract

摘要：

该文研究了一类由曲率控制细胞和组织生长演化的Cauchy问题, 根据支撑函数的定义, 将拟线性退化的演化方程转化成一类非齐次拟线性双曲方程组. 进一步通过对拟线性双曲方程组的解的先验估计, 证明了该双曲曲率流Cauchy问题经典解的生命跨度.

关键词: 曲率控制下细胞和组织的演化, 非齐次拟线性双曲方程组, 先验估计, 生命跨度

Abstract:

In this paper, We consider Cauchy problem for the evolution of cells and tissue during curvature-controlled growth. By the definition of Riemann invariants, the evolution equation can be rewritten as a non-homogeneous quasilinear hyperbolic system. the lifespan of classical solution to the initial value problem is given by a priori estimation of the solution of the quasilinear hyperbolic system.

Key words: The evolution of cells and tissue during curvature-controlled growth, Non-homogeneous quasilinear hyperbolic system, Priori estimation, Lifespan

中图分类号:

O175.2

王增桂. 曲率控制细胞和组织生长演化模型的Cauchy问题[J]. 数学物理学报, 2023, 43(3): 771-784.

Wang Zenggui. Cauchy Problem for the Evolution of Cells and Tissue During Curvature-Controlled Growth[J]. Acta mathematica scientia,Series A, 2023, 43(3): 771-784.

参考文献 27

[1]	Alias M A, Buenzli P R. Modeling the effect of curvature on the collective behavior of cells growing wew tissue. Biophysical Journal, 2017, 112(1): 193-204 doi: 10.1016/j.bpj.2016.11.3203
[2]	Alias M A, Buenzli P R. Osteoblasts infill irregular pores under curvature and porosity controls: a hypothesis-testing analysis of cell behaviours. Biomechanics and Modeling in Mechanobiology, 2018, 17(5): 1357-1371 doi: 10.1007/s10237-018-1031-x pmid: 29846824
[3]	Alias M A, Buenzli P R. A level-set method for the evolution of cells and tissue during curvature-controlled growth. International Journal for Numerical Methods in Biomedical Engineering, 2020, 36(1): e3279
[4]	Gurtin M E, Podio-Guidugli P. A hyperbolic theory for the evolution of plane curves. SIAM J Math Anal, 1991, 22: 575-586 doi: 10.1137/0522036
[5]	Rotstein H G, Brandon S, Novick-Cohen A. Hyperbolic flow by mean curvature. Journal of Crystal Growth, 1999, 198-199: 1256-1261
[6]	Yau S T. Review of geometry and analysis. Asian J Math, 2000, 4: 235-278 doi: 10.4310/AJM.2000.v4.n1.a16
[7]	LeFloch P G, Smoczyk K. The hyperbolic mean curvature flow. Journal De Mathématiques Pures et Appliqués, 2009, 90(6): 591-684
[8]	李秀展, 王增桂. 双曲平均曲率流Cauchy问题经典解的生命跨度. 中国科学: 数学, 2017, 47(8): 953-968 doi: 10.1360/N012016-00188
	Li X Z, Wang Z G. The lifespan of classical solution to the cauchy problem for the hyperbolic mean curvature flow. Sci Sin Math, 2017, 47(8): 953-968 doi: 10.1360/N012016-00188
[9]	LeFloch P G, Yan W P. Nonlinear stability of blow-up solutions to the hyperbolic mean curvature flow. J Differential Equations, 2020, 269(10): 8269-8307 doi: 10.1016/j.jde.2020.05.024
[10]	He C L, Kong D X, Liu K F. Hyperbolic mean curvature flow. J. Differential Equations, 2009, 246: 373-390 doi: 10.1016/j.jde.2008.06.026
[11]	Kong D X, Liu K F, Wang Z G. Hyperbolic mean curvature flow: Evolution of plane curves. Acta Mathematica Scientia (A special issue dedicated to Professor Wu Wenjun's 90th birthday), 2009, 29: 493-614 doi: 10.1016/S0252-9602(09)60049-7
[12]	Kong D X, Wang Z G. Formation of singularities in the motion of plane curves under hyperbolic mean curvature flow. J Differential Equations, 2009, 247: 1694-1719 doi: 10.1016/j.jde.2009.04.016
[13]	He C L, Huang S J, Xing X M. Self-similar solutions to the hyperbolic mean curvature flow. Acta Mathematica Scientia, 2017, 37B(3): 657-667
[14]	Wang Z G. Hyperbolic mean curvature flow with a forcing term: evolution of plane curves. Nonlinear Analysis: Theory, Methods and Applications, 2014, 97: 65-82
[15]	Wang Z G. Symmetries and solutions of hyperbolic mean curvature flow with a constant forcing term. Applied Mathematics and Computation, 2014, 235: 560-566 doi: 10.1016/j.amc.2013.12.134
[16]	王增桂. 带有线性外力场的双曲平均曲率流Cauchy问题经典解的生命跨度. 中国科学:数学, 2013, 43(12): 1193-1208 doi: 10.1360/N012013-00062
	Wang Z G. The lifespan of classical solution to the Cauchy problem for the hyperbolic mean curvature flow with a linear forcing term. Sci Sin Math, 2013, 43(12): 1193-1208 doi: 10.1360/N012013-00062
[17]	Wang Z G. Hyperbolic mean curvature flow in Minkowski space. Nonlinear Analysis: Theory, Methods and Applications, 2014, 94: 259-271
[18]	Mao J. Forced hyperbolic mean curvature flow. Kodai Mathematical Journal, 2012, 35(3): 500-522
[19]	Mao J, Wu C X, Zhou Z. Hyperbolic inverse mean curvature flow. Czechoslovak Mathematical Journal, 2019, (2019): 1-34
[20]	Zhou Z, Wu C X, Mao J. Hyperbolic curve flows in the plane. Journal of Inequalities and Applications, 2019, 2019(1): 1-17 doi: 10.1186/s13660-019-1955-4
[21]	Wang Z G. Life-span of classical solutions to hyperbolic inverse mean curvature flow. Discrete Dynamics in Nature and Society, 2020, 2020: 1-12
[22]	Chou K S, Wo W F. On hyperbolic Gauss curvature flows. J Diff Geom, 2011, 89(3): 455-486
[23]	Wo W F, Ma F Y, Qu C Z. A hyperbolic-type affine invariant curve flow. Communications in Analysis and Geometry, 2014, 22(2): 219-245 doi: 10.4310/CAG.2014.v22.n2.a2
[24]	Wang Z G. A dissipative hyperbolic affine flow. Journal of Mathematical Analysis and Applications, 2018, 465(2): 1094-1111 doi: 10.1016/j.jmaa.2018.05.053
[25]	Notz T. Closed Hypersurfaces Driven by their Mean Curvature and Inner Pressure[D]. Berlin: AlbertEinstein-Institut, 2010
[26]	Yan W P. Motion of closed hypersurfaces in the central force fields. J Differential Equations, 2016, 261(3): 1973-2005 doi: 10.1016/j.jde.2016.04.020
[27]	Ta-Tsien L, Wen-Ci Y. Boundary Value Problems for Quasilinear Hyperbolic Systems. Carolina: Duke Univ, 1985