Chu, Jiawei; Jin, Hai-Yang; Xiang, Tian Global dynamics in a chemotaxis model describing tumor angiogenesis with/without mitosis in any dimension. (English) Zbl 1518.35084 Commun. Math. Sci. 21, No. 4, 1055-1095 (2023). MSC: 35B40 35K51 35K59 92C17 PDFBibTeX XMLCite \textit{J. Chu} et al., Commun. Math. Sci. 21, No. 4, 1055--1095 (2023; Zbl 1518.35084) Full Text: DOI arXiv
Ren, Guoqiang; Xiang, Tian Global solvability and large time behavior in a two-species chemotaxis-consumption model. (English) Zbl 1516.35243 Discrete Contin. Dyn. Syst., Ser. B 28, No. 10, 5325-5354 (2023). MSC: 35K59 35B65 35B40 35A09 35K51 92C17 PDFBibTeX XMLCite \textit{G. Ren} and \textit{T. Xiang}, Discrete Contin. Dyn. Syst., Ser. B 28, No. 10, 5325--5354 (2023; Zbl 1516.35243) Full Text: DOI
Dai, Feng; Xiang, Tian Boundedness and asymptotic stabilization in a two-dimensional Keller-Segel-Navier-Stokes system with sub-logistic source. (English) Zbl 1517.35040 Math. Models Methods Appl. Sci. 32, No. 11, 2237-2294 (2022). MSC: 35B40 35K51 35K59 35Q35 92C17 PDFBibTeX XMLCite \textit{F. Dai} and \textit{T. Xiang}, Math. Models Methods Appl. Sci. 32, No. 11, 2237--2294 (2022; Zbl 1517.35040) Full Text: DOI
Xiang, Tian Finite time blow-up in the higher dimensional parabolic-elliptic-ODE minimal chemotaxis-haptotaxis system. (English) Zbl 1496.35109 J. Differ. Equations 336, 44-72 (2022). MSC: 35B44 35B45 35A01 35A09 35K51 35K59 92C17 PDFBibTeX XMLCite \textit{T. Xiang}, J. Differ. Equations 336, 44--72 (2022; Zbl 1496.35109) Full Text: DOI
Ren, Guoqiang; Xiang, Tian Global solvability in a two-species chemotaxis system with signal production. (English) Zbl 07506765 Acta Appl. Math. 178, Paper No. 12, 26 p. (2022). MSC: 35D30 35K51 35K59 92C17 PDFBibTeX XMLCite \textit{G. Ren} and \textit{T. Xiang}, Acta Appl. Math. 178, Paper No. 12, 26 p. (2022; Zbl 07506765) Full Text: DOI arXiv
Li, Huicong; Xiang, Tian On a cross-diffusive SIS epidemic model with power-like nonlinear incidence. arXiv:2208.09571 Preprint, arXiv:2208.09571 [math.AP] (2022). MSC: 35K57 35Q92 35A01 35B40 92D30 BibTeX Cite \textit{H. Li} and \textit{T. Xiang}, ``On a cross-diffusive SIS epidemic model with power-like nonlinear incidence'', Preprint, arXiv:2208.09571 [math.AP] (2022) Full Text: arXiv OA License
Jin, Hai-Yang; Xiang, Tian Negligibility of haptotaxis effect in a chemotaxis-haptotaxis model. (English) Zbl 1512.35118 Math. Models Methods Appl. Sci. 31, No. 7, 1373-1417 (2021). MSC: 35B44 35A09 35B45 35K51 35K59 92C17 PDFBibTeX XMLCite \textit{H.-Y. Jin} and \textit{T. Xiang}, Math. Models Methods Appl. Sci. 31, No. 7, 1373--1417 (2021; Zbl 1512.35118) Full Text: DOI arXiv
Lin, Ke; Xiang, Tian Strong damping effect of chemo-repulsion prevents blow-up. (English) Zbl 1466.92018 J. Math. Phys. 62, No. 4, Article ID 041508, 29 p. (2021). Reviewer: Piotr Biler (Wrocław) MSC: 92C17 35Q92 35K61 35B40 PDFBibTeX XMLCite \textit{K. Lin} and \textit{T. Xiang}, J. Math. Phys. 62, No. 4, Article ID 041508, 29 p. (2021; Zbl 1466.92018) Full Text: DOI
Wang, Xin; Xiang, Tian; Zhang, Nina Dynamics in a quasilinear parabolic-elliptic Keller-Segel system with generalized logistic source and nonlinear secretion. (English) Zbl 1460.92033 Zheng, Zhiyong (ed.), Proceedings of the first international forum on financial mathematics and financial technology, Suzhou, China, June 29 – July 2, 2019. Singapore: Springer. Financ. Math. Fintech, 177-206 (2021). MSC: 92C17 35Q92 PDFBibTeX XMLCite \textit{X. Wang} et al., in: Proceedings of the first international forum on financial mathematics and financial technology, Suzhou, China, June 29 -- July 2, 2019. Singapore: Springer. 177--206 (2021; Zbl 1460.92033) Full Text: DOI
Ren, Guoqiang; Xiang, Tian Global solvability and asymptotical behavior in a two-species chemotaxis model with signal absorption. arXiv:2102.03713 Preprint, arXiv:2102.03713 [math.AP] (2021). MSC: 35K59 35K57 BibTeX Cite \textit{G. Ren} and \textit{T. Xiang}, ``Global solvability and asymptotical behavior in a two-species chemotaxis model with signal absorption'', Preprint, arXiv:2102.03713 [math.AP] (2021) Full Text: arXiv OA License
Li, Huicong; Peng, Rui; Xiang, Tian Dynamics and asymptotic profiles of endemic equilibrium for two frequency-dependent SIS epidemic models with cross-diffusion. (English) Zbl 1504.35072 Eur. J. Appl. Math. 31, No. 1, 26-56 (2020). MSC: 35B40 35K51 35K57 92D25 PDFBibTeX XMLCite \textit{H. Li} et al., Eur. J. Appl. Math. 31, No. 1, 26--56 (2020; Zbl 1504.35072) Full Text: DOI arXiv
Lin, Ke; Xiang, Tian On boundedness, blow-up and convergence in a two-species and two-stimuli chemotaxis system with/without loop. (English) Zbl 1443.35060 Calc. Var. Partial Differ. Equ. 59, No. 4, Paper No. 108, 35 p. (2020). MSC: 35K51 35Q92 35B25 35B44 35K59 92C17 92D25 PDFBibTeX XMLCite \textit{K. Lin} and \textit{T. Xiang}, Calc. Var. Partial Differ. Equ. 59, No. 4, Paper No. 108, 35 p. (2020; Zbl 1443.35060) Full Text: DOI arXiv
Xiang, Tian; Zheng, Jiashan A new result for 2D boundedness of solutions to a chemotaxis-haptotaxis model with/without sub-logistic source. (English) Zbl 1425.35110 Nonlinearity 32, No. 12, 4890-4911 (2019). MSC: 35K59 35Q92 35K55 35K20 92C17 PDFBibTeX XMLCite \textit{T. Xiang} and \textit{J. Zheng}, Nonlinearity 32, No. 12, 4890--4911 (2019; Zbl 1425.35110) Full Text: DOI arXiv
Lin, Ke; Xiang, Tian On global solutions and blow-up for a short-ranged chemical signaling loop. (English) Zbl 1417.35066 J. Nonlinear Sci. 29, No. 2, 551-591 (2019). MSC: 35K55 35B40 35B35 92C17 35Q92 PDFBibTeX XMLCite \textit{K. Lin} and \textit{T. Xiang}, J. Nonlinear Sci. 29, No. 2, 551--591 (2019; Zbl 1417.35066) Full Text: DOI
Jin, Hai-Yang; Xiang, Tian Convergence rates of solutions for a two-species chemotaxis-Navier-Stokes system with competitive kinetics. (English) Zbl 1420.35439 Discrete Contin. Dyn. Syst., Ser. B 24, No. 4, 1919-1942 (2019). Reviewer: Eugene Postnikov (Kursk) MSC: 35Q92 35B40 35K55 35B44 35K57 92C17 35Q35 35B65 PDFBibTeX XMLCite \textit{H.-Y. Jin} and \textit{T. Xiang}, Discrete Contin. Dyn. Syst., Ser. B 24, No. 4, 1919--1942 (2019; Zbl 1420.35439) Full Text: DOI arXiv
Xiang, Tian Dynamics in a parabolic-elliptic chemotaxis system with growth source and nonlinear secretion. (English) Zbl 1401.35189 Commun. Pure Appl. Anal. 18, No. 1, 255-284 (2019). MSC: 35K57 35K51 37K50 35A01 92C17 PDFBibTeX XMLCite \textit{T. Xiang}, Commun. Pure Appl. Anal. 18, No. 1, 255--284 (2019; Zbl 1401.35189) Full Text: DOI
Jin, Hai-Yang; Xiang, Tian Repulsion effects on boundedness in a quasilinear attraction-repulsion chemotaxis model in higher dimensions. (English) Zbl 1404.35229 Discrete Contin. Dyn. Syst., Ser. B 23, No. 8, 3071-3085 (2018). MSC: 35K51 35K59 35B45 35A01 35Q92 92C17 PDFBibTeX XMLCite \textit{H.-Y. Jin} and \textit{T. Xiang}, Discrete Contin. Dyn. Syst., Ser. B 23, No. 8, 3071--3085 (2018; Zbl 1404.35229) Full Text: DOI
Xiang, Tian Chemotactic aggregation versus logistic damping on boundedness in the 3D minimal Keller-Segel model. (English) Zbl 1397.35125 SIAM J. Appl. Math. 78, No. 5, 2420-2438 (2018). Reviewer: Piotr Biler (Wrocław) MSC: 35K51 35Q92 35K57 35B30 35B44 35A01 92C17 PDFBibTeX XMLCite \textit{T. Xiang}, SIAM J. Appl. Math. 78, No. 5, 2420--2438 (2018; Zbl 1397.35125) Full Text: DOI
Xiang, Tian Sub-logistic source can prevent blow-up in the 2D minimal Keller-Segel chemotaxis system. (English) Zbl 1395.92025 J. Math. Phys. 59, No. 8, 081502, 11 p. (2018). MSC: 92C17 92B10 35K20 35B44 PDFBibTeX XMLCite \textit{T. Xiang}, J. Math. Phys. 59, No. 8, 081502, 11 p. (2018; Zbl 1395.92025) Full Text: DOI arXiv
Jin, Hai-Yang; Xiang, Tian Chemotaxis effect vs. logistic damping on boundedness in the 2-D minimal Keller-Segel model. (Effet chimiotaxique contre amortissement logistique pour borner les solutions du modèle de Keller-Segel minimal en dimension 2.) (English. French summary) Zbl 1397.92096 C. R., Math., Acad. Sci. Paris 356, No. 8, 875-885 (2018). MSC: 92C17 35K57 PDFBibTeX XMLCite \textit{H.-Y. Jin} and \textit{T. Xiang}, C. R., Math., Acad. Sci. Paris 356, No. 8, 875--885 (2018; Zbl 1397.92096) Full Text: DOI arXiv
Xiang, Tian How strong a logistic damping can prevent blow-up for the minimal Keller-Segel chemotaxis system? (English) Zbl 1380.35032 J. Math. Anal. Appl. 459, No. 2, 1172-1200 (2018). Reviewer: Piotr Biler (Wrocław) MSC: 35B44 35K51 35Q92 92C17 PDFBibTeX XMLCite \textit{T. Xiang}, J. Math. Anal. Appl. 459, No. 2, 1172--1200 (2018; Zbl 1380.35032) Full Text: DOI arXiv
Xiang, Tian Global dynamics for a diffusive predator-prey model with prey-taxis and classical Lotka-Volterra kinetics. (English) Zbl 1516.35096 Nonlinear Anal., Real World Appl. 39, 278-299 (2018). MSC: 35B40 35K51 35K59 92D25 PDFBibTeX XMLCite \textit{T. Xiang}, Nonlinear Anal., Real World Appl. 39, 278--299 (2018; Zbl 1516.35096) Full Text: DOI
Cantrell, Robert Stephen; Cao, Xinru; Lam, King-Yeung; Xiang, Tian A PDE model of intraguild predation with cross-diffusion. (English) Zbl 1516.35239 Discrete Contin. Dyn. Syst., Ser. B 22, No. 10, 3653-3661 (2017). MSC: 35K59 35K45 92D15 92D25 PDFBibTeX XMLCite \textit{R. S. Cantrell} et al., Discrete Contin. Dyn. Syst., Ser. B 22, No. 10, 3653--3661 (2017; Zbl 1516.35239) Full Text: DOI
Jin, Hai-Yang; Xiang, Tian Boundedness and exponential convergence in a chemotaxis model for tumor invasion. (English) Zbl 1364.35127 Nonlinearity 29, No. 12, 3579-3596 (2016). MSC: 35K51 35B40 35B44 35K57 35Q92 92C17 PDFBibTeX XMLCite \textit{H.-Y. Jin} and \textit{T. Xiang}, Nonlinearity 29, No. 12, 3579--3596 (2016; Zbl 1364.35127) Full Text: DOI arXiv
Xiang, Tian; Georgiev, Svetlin Georgiev Noncompact-type Krasnoselskii fixed-point theorems and their applications. (English) Zbl 1347.35011 Math. Methods Appl. Sci. 39, No. 4, 833-863 (2016). Reviewer: Valerii V. Obukhovskij (Voronezh) MSC: 35A16 47H10 35F20 35M12 35R10 39A23 82C70 PDFBibTeX XMLCite \textit{T. Xiang} and \textit{S. G. Georgiev}, Math. Methods Appl. Sci. 39, No. 4, 833--863 (2016; Zbl 1347.35011) Full Text: DOI
Xiang, Tian On a class of Keller-Segel chemotaxis systems with cross-diffusion. (English) Zbl 1333.35096 J. Differ. Equations 259, No. 8, 4273-4326 (2015). Reviewer: Philippe Laurençot (Toulouse) MSC: 35K51 35B32 35B35 35Q92 92C17 PDFBibTeX XMLCite \textit{T. Xiang}, J. Differ. Equations 259, No. 8, 4273--4326 (2015; Zbl 1333.35096) Full Text: DOI
Xiang, Tian Boundedness and global existence in the higher-dimensional parabolic – parabolic chemotaxis system with/without growth source. (English) Zbl 1323.35072 J. Differ. Equations 258, No. 12, 4275-4323 (2015). Reviewer: Piotr Biler (Wroclaw) MSC: 35K51 92C17 35K59 35B44 PDFBibTeX XMLCite \textit{T. Xiang}, J. Differ. Equations 258, No. 12, 4275--4323 (2015; Zbl 1323.35072) Full Text: DOI
Wang, Zhi-an; Xiang, Tian A class of chemotaxis systems with growth source and nonlinear secretion. arXiv:1510.07204 Preprint, arXiv:1510.07204 [math.AP] (2015). MSC: 35K57 35K51 92C17 BibTeX Cite \textit{Z.-a. Wang} and \textit{T. Xiang}, ``A class of chemotaxis systems with growth source and nonlinear secretion'', Preprint, arXiv:1510.07204 [math.AP] (2015) Full Text: arXiv OA License
Zhang, Ziheng; Xiang, Tian; Yuan, Rong Homoclinic solutions for subquadratic Hamiltonian systems without coercive conditions. (English) Zbl 1357.34082 Taiwanese J. Math. 18, No. 4, 1089-1105 (2014). MSC: 34C37 35A15 35B38 PDFBibTeX XMLCite \textit{Z. Zhang} et al., Taiwanese J. Math. 18, No. 4, 1089--1105 (2014; Zbl 1357.34082) Full Text: DOI
Xiang, Tian On effects of sampling radius for the nonlocal Patlak-Keller-Segel chemotaxis model. (English) Zbl 1307.35038 Discrete Contin. Dyn. Syst. 34, No. 11, 4911-4946 (2014). MSC: 35B35 35K57 35B40 92C17 35B32 35K45 35B36 PDFBibTeX XMLCite \textit{T. Xiang}, Discrete Contin. Dyn. Syst. 34, No. 11, 4911--4946 (2014; Zbl 1307.35038) Full Text: DOI
Xiang, Tian A study on the positive nonconstant steady states of nonlocal chemotaxis systems. (English) Zbl 1301.92007 Discrete Contin. Dyn. Syst., Ser. B 18, No. 9, 2457-2485 (2013). MSC: 92C17 35B32 35K51 35K57 PDFBibTeX XMLCite \textit{T. Xiang}, Discrete Contin. Dyn. Syst., Ser. B 18, No. 9, 2457--2485 (2013; Zbl 1301.92007) Full Text: DOI