杨冰, 李功胜
杨冰, 李功胜. 一个分数阶生长-抑制系统的参数反问题[J]. 计算数学, 2023, 45(2): 215-229.
Yang Bing, Li Gongsheng. AN INVERSE COEFFICIENT PROBLEM FOR A FRACTIONAL-ORDER ACTIVATOR-INHIBITOR SYSTEM[J]. Mathematica Numerica Sinica, 2023, 45(2): 215-229.
Yang Bing, Li Gongsheng
MR(2010)主题分类:
分享此文:
[1] Turing A M. The chemical basis of morphogebesis[J]. Philosophical Transactions of the Royal Society of London B, 1952, 237:37-72. [2] 陈兰荪.数学生态学模型与研究方法[M].北京:科学出版社, 1988. [3] Zhao X Q. Dynamical Systems in Population Biology[M]. Springer-Verlag, New York, Inc., 2003. [4] 欧阳颀.非线性科学与斑图动力学导论[M].北京:北京大学出版社, 2010. [5] Bai L and Wang K. Giplin-Ayala model with spatial diffusion and its optimal harvesting policy[J]. Appl. Math. Comput., 2005, 171:531-546. [6] Chakraborty A, Singh M, Lucy D and Ridland P. Predator-prey model with prey-taxis and diffusion[J]. Math. Comput. Modelling, 2007, 46:482-498. [7] Jin Y and Zhao X Q. Bistable waves for a class of cooperative reaction-diffusion systems[J]. J. Biol. Dynamics, 2008, 2:196-207. [8] 杨文彬, 吴建华. 空间齐次和非齐次下活化-抑制模型动力学分析[J].数学物理学报, 2017, 37A(2):390-400. [9] Li B W and Wang J. Anomalous heat conduction and anomalous diffusion in one-dimensional systems[J]. Phys. Rev. Lett., 2003, 91:044301. [10] Golovin A A, Matkowsky B J and Volpert V A. Turing pattern formation in the brusselator model with superdiffusion[J]. SIAM J. Appl. Math., 2008, 69:251-272. [11] 陈文, 孙洪广, 李西成, 等.力学与工程问题的分数阶导数建模[M].北京:科学出版社, 2010. [12] Gambino G, Lombardo M C, Sammartino M and Sciacca V. Turing pattern formation in the Brusselator system with nonlinear diffusion[J]. Phys. Rev. E, 2013, 88:042925. [13] Podlubny I. Fractional Differential Equations[M]. Academic Press, San Diego, 1999. [14] Kilbas A A, Srivastava H M and Trujillo J J. Theory and Applications of Fractional Differential Equations[M]. Elsevier, Amsterdam, 2006. [15] Henry B I and Wearne S L. Existence of Turing instabilities in a two-species fractional reactiondiffusion system[J]. SIAM J Appl. Math., 2002, 62:870-887. [16] Henry B I and Langlands A M. Turing pattern formation in fractional activator-inhibitor system[J]. Physical Review E, 2005, 72:026101. [17] Gafiychuk V V and Datsko B. Pattern formation in a fractional reaction-diffusion system[J]. Physica A, 2006, 365:300-306. [18] Yana N and Michael J W. Dynamics and stability of spike-type solutions to a one dimensional Gierer-Meinhardt model with sub-diffusion[J]. Physica D, 2012, 241:947-963. [19] Datsko B, Kutniv M and Wloch A. Mathematical modelling of pattern formation in activatorinhibitor reaction-diffusion systems with anomalous diffusion[J]. Journal of Mathematical Chemistry, 2020, 58:612-631. [20] Rivero M, Trujillo J J, Vazquez L and Velasco P M. Fractional dynamics of populations[J]. Applied Mathematics and Computation, 2011, 218:1089-1095. [21] Cheng J, Nakagawa J, Yamamoto M and Yamazaki T. Uniqueness in an inverse problem for a one-dimensional fractional diffusion equation[J]. Inverse Problems, 2009, 25:115002. [22] Sakamoto K and Yamamoto M. Initial value/boundary value problems for fractional diffusionwave equations and applications to some inverse problems[J]. Journal of Mathematical Analysis and Applications, 2011, 382:426-447. [23] Li G S, Zhang D L, Jia X Z and Yamamoto M. Simultaneous inversion for the space-dependent diffusion coefficient and the fractional order in the time-fractional diffusion equation[J]. Inverse Problems, 2013, 29:065014. [24]贾现正, 张大利, 李功胜, 池光胜, 李慧玲.空间-时间分数阶变系数对流扩散方程微分阶数的数值反演[J].计算数学, 2014, 36(2):113-132. [25] Jin B T and Rundell W. A tutorial on inverse problems for anomalous diffusion processes[J]. Inverse Problems, 2015, 31:035003. [26] Wei T, Li X L and Li Y S. An inverse time-dependent source problem for a time-fractional diffusion equation[J]. Inverse problems, 2016, 32:085003. [27] Kian Y, Oksanen L, Soccorsi E and Yamamoto M. Global uniqueness in an inverse problem for time fractional diffusion equations[J]. Journal of Differential Equations, 2018, 264:1146-1170. [28] Zheng X C, Cheng J and Wang H. Uniqueness of determining the variable fractional order in variable-order time-fractional diffusion equations[J]. Inverse Problms, 2019, 35:125002. [29] Li Z Y, Fujishiro K and Li G S. Uniqueness in the inversion of distributed orders in ultraslow diffusion equations[J]. Journal of Computational and Applied Mathematics, 2020, 369:112564. [30] Yamamoto M. Uniqueness in determining fractional orders of derivatives and initial values[J]. Inverse Problems, 2021, 37:095006. [31] Fife P C and Arizona T. On modelling pattern formation by activator-inhibitor systems[J]. J. Math. Biology, 1977, 4:353-362. [32] Garvie M R, Maini P K and Trenchea C. An efficient and robust numerical algorithm for estimating parameters in Turing systems[J]. J. Comput. Phys., 2010, 229:353-362. [33] Garvie M R and Trenchea C. Identification of space-time distributed parameters in the GiererMeinhardt reaction-diffusion system[J]. SIAM J. Appl. Math., 2014, 74:147-166. [34] Kubica A, Ryszewska K and Yamamoto M. Theory of Time-Fractional Differential Equations an Introduction[M]. Springer, Berlin, 2020. [35] Sperb R P. Maximum Principles and Their Applications[M]. Academic Press, New York, 1981. [36] 孙志忠, 高广花, 分数阶微分方程的差分方法(第二版)[M].北京:科学出版社, 2020. [37] Zhang D L, Li G S, Jia X Z and Li H L. Simultaneous inversion for space-dependent diffusion coefficient and source magnitude in the time fractional diffusion equation[J]. Journal of Mathematics Research, 2013, 5:65-78. |
[1] | 王嘉华, 李宏. 粘弹性波动方程的H$^1$-Galerkin时空混合有限元分裂格式[J]. 计算数学, 2023, 45(2): 177-196. |
[2] | 王琳, 许珊珊, 王文强. 非线性随机分数阶延迟积分微分方程Euler-Maruyama方法的强收敛性[J]. 计算数学, 2023, 45(1): 57-73. |
[3] | 朱梦姣, 王文强. 非线性随机分数阶微分方程Euler方法的弱收敛性[J]. 计算数学, 2021, 43(1): 87-109. |
[4] | 刘金存, 李宏, 刘洋, 何斯日古楞. 非线性分数阶反应扩散方程组的间断时空有限元方法[J]. 计算数学, 2016, 38(2): 143-160. |
[5] | 崔霞, 岳晶岩. 守恒型扩散方程非线性离散格式的性质分析和快速求解[J]. 计算数学, 2015, 37(3): 227-246. |
[6] | 贾现正, 张大利, 李功胜, 池光胜, 李慧玲. 空间-时间分数阶变系数对流扩散方程微分阶数的数值反演[J]. 计算数学, 2014, 36(2): 113-132. |
[7] | 罗振东, 高骏强, 孙萍, 安静. 交通流模型基于特征投影分解技术的外推降维有限差分格式[J]. 计算数学, 2013, 35(2): 159-170. |
[8] | 张春赛, 胡良剑. 时滞均值回复θ过程及其数值解的收敛性[J]. 计算数学, 2011, 33(2): 185-198. |
[9] | 吴宏伟. 关于广义KPP方程的数值解[J]. 计算数学, 2009, 31(2): 137-150. |
[10] | 刘伟,袁益让,. 三维半导体器件问题在时空局部加密复合网格上的有限差分格式[J]. 计算数学, 2006, 28(2): 175-188. |
[11] | 汤华中. 一个刚性守恒律方程组的全隐式差分方法[J]. 计算数学, 2001, 23(2): 129-138. |
[12] | 袁光伟. 非线性抛物组非均匀网格差分解的唯一性和稳定性[J]. 计算数学, 2000, 22(2): 139-150. |
阅读次数 | ||||||
全文 |
|
|||||
摘要 |
|
|||||