Chen, Miaochao; Chen, Fangqi; Lu, Shengqi; Liu, Qilin Blow-up criteria for a Keller-Segel-Navier-Stokes system in a bounded domain. (English) Zbl 07644560 Appl. Math. Lett. 139, Article ID 108536, 8 p. (2023). Reviewer: Yuanyuan Ke (Beijing) MSC: 35B44 35K51 35K59 35Q30 92C17 PDF BibTeX XML Cite \textit{M. Chen} et al., Appl. Math. Lett. 139, Article ID 108536, 8 p. (2023; Zbl 07644560) Full Text: DOI OpenURL
Liu, Ji A two-dimensional Keller-Segel-Navier-Stokes system with logarithmic sensitivity: generalized solutions and classical solutions. (English) Zbl 07620709 Calc. Var. Partial Differ. Equ. 62, No. 1, Paper No. 23, 37 p. (2023). MSC: 35D30 35A09 35K51 35K59 35Q35 92C17 PDF BibTeX XML Cite \textit{J. Liu}, Calc. Var. Partial Differ. Equ. 62, No. 1, Paper No. 23, 37 p. (2023; Zbl 07620709) Full Text: DOI OpenURL
Kurt, Halil Ibrahim; Shen, Wenxian Chemotaxis systems with singular sensitivity and logistic source: boundedness, persistence, absorbing set, and entire solutions. (English) Zbl 1501.35066 Nonlinear Anal., Real World Appl. 69, Article ID 103762, 27 p. (2023). MSC: 35B40 35K51 35K59 92C17 PDF BibTeX XML Cite \textit{H. I. Kurt} and \textit{W. Shen}, Nonlinear Anal., Real World Appl. 69, Article ID 103762, 27 p. (2023; Zbl 1501.35066) Full Text: DOI arXiv OpenURL
Zhang, Wenji Global generalized solvability in the Keller-Segel system with singular sensitivity and arbitrary superlinear degradation. (English) Zbl 07613221 Discrete Contin. Dyn. Syst., Ser. B 28, No. 2, 1267-1278 (2023). Reviewer: Piotr Biler (Wrocław) MSC: 35Q92 35K55 35B40 92C17 PDF BibTeX XML Cite \textit{W. Zhang}, Discrete Contin. Dyn. Syst., Ser. B 28, No. 2, 1267--1278 (2023; Zbl 07613221) Full Text: DOI OpenURL
Rodriguez, Nancy; Winkler, Michael On the global existence and qualitative behaviour of one-dimensional solutions to a model for urban crime. (English) Zbl 07629707 Eur. J. Appl. Math. 33, No. 5, 919-959 (2022). MSC: 35Q91 35B40 35K55 91D10 35A01 35A09 PDF BibTeX XML Cite \textit{N. Rodriguez} and \textit{M. Winkler}, Eur. J. Appl. Math. 33, No. 5, 919--959 (2022; Zbl 07629707) Full Text: DOI arXiv OpenURL
Wu, Chun Boundedness in a chemotaxis-consumption system with singular sensitivity. (English) Zbl 1501.35075 Result. Math. 77, No. 6, Paper No. 234, 31 p. (2022). MSC: 35B40 35K51 35K59 92C17 35Q92 PDF BibTeX XML Cite \textit{C. Wu}, Result. Math. 77, No. 6, Paper No. 234, 31 p. (2022; Zbl 1501.35075) Full Text: DOI OpenURL
Yang, Lan; Yang, Xujie Global existence in a two-dimensional nonlinear diffusion model for urban crime propagation. (English) Zbl 1496.35229 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 224, Article ID 113086, 32 p. (2022). MSC: 35K51 35K59 35Q91 92C17 PDF BibTeX XML Cite \textit{L. Yang} and \textit{X. Yang}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 224, Article ID 113086, 32 p. (2022; Zbl 1496.35229) Full Text: DOI OpenURL
Zheng, Jiashan; Xie, Jianing Global classical solutions of Keller-Segel-(Navier)-Stokes system with nonlinear motility functions. (English) Zbl 1494.35003 J. Math. Anal. Appl. 514, No. 1, Article ID 126272, 23 p. (2022). Reviewer: Yuanyuan Ke (Beijing) MSC: 35A01 35K51 35K59 35Q35 92C17 PDF BibTeX XML Cite \textit{J. Zheng} and \textit{J. Xie}, J. Math. Anal. Appl. 514, No. 1, Article ID 126272, 23 p. (2022; Zbl 1494.35003) Full Text: DOI OpenURL
Xie, Li; Ruan, Shigui On a macrophage and tumor cell chemotaxis system with both paracrine and autocrine loops. (English) Zbl 1487.35380 Commun. Pure Appl. Anal. 21, No. 4, 1447-1479 (2022). Reviewer: Piotr Biler (Wrocław) MSC: 35Q92 35K55 35B40 PDF BibTeX XML Cite \textit{L. Xie} and \textit{S. Ruan}, Commun. Pure Appl. Anal. 21, No. 4, 1447--1479 (2022; Zbl 1487.35380) Full Text: DOI OpenURL
Jiang, Yongfeng; Yang, Lan Global solvability and stabilization in a three-dimensional cross-diffusion system modeling urban crime propagation. (English) Zbl 1486.35258 Acta Appl. Math. 178, Paper No. 11, 40 p. (2022). MSC: 35K51 35K59 35B40 35D30 35Q91 PDF BibTeX XML Cite \textit{Y. Jiang} and \textit{L. Yang}, Acta Appl. Math. 178, Paper No. 11, 40 p. (2022; Zbl 1486.35258) Full Text: DOI OpenURL
Chen, Miaochao; Lu, Shengqi; Liu, Qilin Uniqueness of weak solutions to a Keller-Segel-Navier-Stokes model with a logistic source. (English) Zbl 07478519 Appl. Math., Praha 67, No. 1, 93-101 (2022). MSC: 22E46 53C35 57S20 35Q30 PDF BibTeX XML Cite \textit{M. Chen} et al., Appl. Math., Praha 67, No. 1, 93--101 (2022; Zbl 07478519) Full Text: DOI OpenURL
Winkler, Michael Unlimited growth in logarithmic Keller-Segel systems. (English) Zbl 1480.35383 J. Differ. Equations 309, 74-97 (2022). Reviewer: Piotr Biler (Wrocław) MSC: 35Q92 35B44 35B25 35K59 92C17 PDF BibTeX XML Cite \textit{M. Winkler}, J. Differ. Equations 309, 74--97 (2022; Zbl 1480.35383) Full Text: DOI OpenURL
Chen, Miaochao; Lu, Shengqi; Liu, Qilin Uniqueness of weak solutions to a Keller-Segel-Navier-Stokes system. (English) Zbl 1475.35002 Appl. Math. Lett. 121, Article ID 107417, 7 p. (2021). MSC: 35A02 35K51 35K59 35Q30 92C17 PDF BibTeX XML Cite \textit{M. Chen} et al., Appl. Math. Lett. 121, Article ID 107417, 7 p. (2021; Zbl 1475.35002) Full Text: DOI OpenURL
Xu, Wei; Sun, Tao Global solvability to a 3D chemotaxis-fluid model with matrix-valued supercritical sensitivities. (English) Zbl 1471.76098 Acta Appl. Math. 173, Paper No. 12, 31 p. (2021). MSC: 76Z05 76R50 76S05 92C17 35Q30 35Q92 PDF BibTeX XML Cite \textit{W. Xu} and \textit{T. Sun}, Acta Appl. Math. 173, Paper No. 12, 31 p. (2021; Zbl 1471.76098) Full Text: DOI OpenURL
Jiang, Jie; Laurençot, Philippe Global existence and uniform boundedness in a chemotaxis model with signal-dependent motility. (English) Zbl 1472.35401 J. Differ. Equations 299, 513-541 (2021). Reviewer: Piotr Biler (Wrocław) MSC: 35Q92 35K65 35B40 35B51 PDF BibTeX XML Cite \textit{J. Jiang} and \textit{P. Laurençot}, J. Differ. Equations 299, 513--541 (2021; Zbl 1472.35401) Full Text: DOI arXiv OpenURL
Cao, Chongsheng; Kang, Hao Global well-posedness of 2D chemotaxis Euler fluid systems. (English) Zbl 1475.35250 J. Differ. Equations 294, 251-264 (2021). MSC: 35Q31 35Q35 76B03 35B65 92C17 35A01 35A02 PDF BibTeX XML Cite \textit{C. Cao} and \textit{H. Kang}, J. Differ. Equations 294, 251--264 (2021; Zbl 1475.35250) Full Text: DOI OpenURL
Wang, Zhi-An; Zheng, Jiashan Global boundedness of the fully parabolic Keller-Segel system with signal-dependent motilities. (English) Zbl 1469.35113 Acta Appl. Math. 171, Paper No. 25, 20 p. (2021). MSC: 35K51 35K59 92C17 PDF BibTeX XML Cite \textit{Z.-A. Wang} and \textit{J. Zheng}, Acta Appl. Math. 171, Paper No. 25, 20 p. (2021; Zbl 1469.35113) Full Text: DOI arXiv OpenURL
Arumugam, Gurusamy; Tyagi, Jagmohan Keller-Segel chemotaxis models: a review. (English) Zbl 1464.35001 Acta Appl. Math. 171, Paper No. 6, 82 p. (2021). MSC: 35-02 35A35 35D30 35B40 35B44 35K51 35K59 65N30 65M08 65M06 PDF BibTeX XML Cite \textit{G. Arumugam} and \textit{J. Tyagi}, Acta Appl. Math. 171, Paper No. 6, 82 p. (2021; Zbl 1464.35001) Full Text: DOI OpenURL
Ahn, Jaewook; Kang, Kyungkeun; Lee, Jihoon Global well-posedness of logarithmic Keller-Segel type systems. (English) Zbl 1464.35348 J. Differ. Equations 287, 185-211 (2021). MSC: 35Q92 35Q91 92C17 91D10 35K57 35B40 35B65 35A09 35A01 35A02 PDF BibTeX XML Cite \textit{J. Ahn} et al., J. Differ. Equations 287, 185--211 (2021; Zbl 1464.35348) Full Text: DOI arXiv OpenURL
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 PDF BibTeX XML Cite \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 OpenURL
Kurt, Halil Ibrahim; Shen, Wenxian Finite-time blow-up prevention by logistic source in parabolic-elliptic chemotaxis models with singular sensitivity in any dimensional setting. (English) Zbl 1455.35269 SIAM J. Math. Anal. 53, No. 1, 973-1003 (2021). MSC: 35Q92 92C17 35K55 35B44 35K51 35K57 PDF BibTeX XML Cite \textit{H. I. Kurt} and \textit{W. Shen}, SIAM J. Math. Anal. 53, No. 1, 973--1003 (2021; Zbl 1455.35269) Full Text: DOI arXiv OpenURL
Fan, Jishan; Li, Fucai Global strong solutions to a coupled chemotaxis-fluid model with subcritical sensitivity. (English) Zbl 1459.35361 Acta Appl. Math. 169, 767-791 (2020). MSC: 35Q92 92C17 35B65 35D35 35Q35 PDF BibTeX XML Cite \textit{J. Fan} and \textit{F. Li}, Acta Appl. Math. 169, 767--791 (2020; Zbl 1459.35361) Full Text: DOI OpenURL
Winkler, Michael Blow-up profiles and life beyond blow-up in the fully parabolic Keller-Segel system. (English) Zbl 1459.92019 J. Anal. Math. 141, No. 2, 585-624 (2020). MSC: 92C17 35Q92 PDF BibTeX XML Cite \textit{M. Winkler}, J. Anal. Math. 141, No. 2, 585--624 (2020; Zbl 1459.92019) Full Text: DOI OpenURL
Lindstrom, Michael R.; Bertozzi, Andrea L. Qualitative features of a nonlinear, nonlocal, agent-based PDE model with applications to homelessness. (English) Zbl 1455.35262 Math. Models Methods Appl. Sci. 30, No. 10, 1863-1891 (2020). MSC: 35Q91 91D10 91B69 35B10 35B35 35B50 35K55 65M20 65N06 91-08 PDF BibTeX XML Cite \textit{M. R. Lindstrom} and \textit{A. L. Bertozzi}, Math. Models Methods Appl. Sci. 30, No. 10, 1863--1891 (2020; Zbl 1455.35262) Full Text: DOI OpenURL
Black, Tobias; Lankeit, Johannes; Mizukami, Masaaki Stabilization in the Keller-Segel system with signal-dependent sensitivity. (English) Zbl 1461.35045 Appl. Anal. 99, No. 16, 2877-2891 (2020). Reviewer: Neng Zhu (Nanchang) MSC: 35B40 35K51 92C17 35Q92 35K59 PDF BibTeX XML Cite \textit{T. Black} et al., Appl. Anal. 99, No. 16, 2877--2891 (2020; Zbl 1461.35045) Full Text: DOI arXiv OpenURL
Winkler, Michael Can simultaneous density-determined enhancement of diffusion and cross-diffusion foster boundedness in Keller-Segel type systems involving signal-dependent motilities? (English) Zbl 1454.35224 Nonlinearity 33, No. 12, 6590-6623 (2020). Reviewer: Piotr Biler (Wrocław) MSC: 35K65 35K57 35B40 92C17 35K51 PDF BibTeX XML Cite \textit{M. Winkler}, Nonlinearity 33, No. 12, 6590--6623 (2020; Zbl 1454.35224) Full Text: DOI OpenURL
Jin, Hai-Yang; Wang, Zhi-An Critical mass on the Keller-Segel system with signal-dependent motility. (English) Zbl 1448.35516 Proc. Am. Math. Soc. 148, No. 11, 4855-4873 (2020). Reviewer: Piotr Biler (Wrocław) MSC: 35Q92 35K55 35B40 35B44 92C17 PDF BibTeX XML Cite \textit{H.-Y. Jin} and \textit{Z.-A. Wang}, Proc. Am. Math. Soc. 148, No. 11, 4855--4873 (2020; Zbl 1448.35516) Full Text: DOI arXiv OpenURL
Chen, Miaochao; Lu, Shengqi; Liu, Qilin Uniform regularity for a Keller-Segel-Navier-Stokes system. (English) Zbl 1441.35019 Appl. Math. Lett. 107, Article ID 106476, 6 p. (2020). MSC: 35B20 92C17 35Q30 35B40 PDF BibTeX XML Cite \textit{M. Chen} et al., Appl. Math. Lett. 107, Article ID 106476, 6 p. (2020; Zbl 1441.35019) Full Text: DOI OpenURL
Lankeit, Johannes; Viglialoro, Giuseppe Global existence and boundedness of solutions to a chemotaxis-consumption model with singular sensitivity. (English) Zbl 1439.35243 Acta Appl. Math. 167, 75-97 (2020). MSC: 35K55 35Q92 35A01 35K51 92C17 PDF BibTeX XML Cite \textit{J. Lankeit} and \textit{G. Viglialoro}, Acta Appl. Math. 167, 75--97 (2020; Zbl 1439.35243) Full Text: DOI arXiv Link OpenURL
Liu, Dongmei Global solutions in a fully parabolic chemotaxis system with singular sensitivity and nonlinear signal production. (English) Zbl 1439.92043 J. Math. Phys. 61, No. 2, 021503, 4 p. (2020). MSC: 92C17 35Q92 PDF BibTeX XML Cite \textit{D. Liu}, J. Math. Phys. 61, No. 2, 021503, 4 p. (2020; Zbl 1439.92043) Full Text: DOI OpenURL
Black, Tobias Global generalized solutions to a parabolic-elliptic Keller-Segel system with singular sensitivity. (English) Zbl 1439.35486 Discrete Contin. Dyn. Syst., Ser. S 13, No. 2, 119-137 (2020). Reviewer: Piotr Biler (Wrocław) MSC: 35Q92 35D99 35K55 92C17 35A01 PDF BibTeX XML Cite \textit{T. Black}, Discrete Contin. Dyn. Syst., Ser. S 13, No. 2, 119--137 (2020; Zbl 1439.35486) Full Text: DOI arXiv OpenURL
Ahn, Jaewook; Kang, Kyungkeun; Lee, Jihoon Eventual smoothness and stabilization of global weak solutions in parabolic-elliptic chemotaxis systems with logarithmic sensitivity. (English) Zbl 1437.35060 Nonlinear Anal., Real World Appl. 49, 312-330 (2019). MSC: 35B40 35B65 35K51 35K58 92C17 PDF BibTeX XML Cite \textit{J. Ahn} et al., Nonlinear Anal., Real World Appl. 49, 312--330 (2019; Zbl 1437.35060) Full Text: DOI OpenURL
Biler, Piotr Blowup of solutions for nonlinear nonlocal heat equations. (English) Zbl 1418.35221 Monatsh. Math. 189, No. 4, 611-624 (2019). MSC: 35K55 35B44 PDF BibTeX XML Cite \textit{P. Biler}, Monatsh. Math. 189, No. 4, 611--624 (2019; Zbl 1418.35221) Full Text: DOI arXiv OpenURL
Ahn, Jaewook Global well-posedness and asymptotic stabilization for chemotaxis system with signal-dependent sensitivity. (English) Zbl 1415.35036 J. Differ. Equations 266, No. 10, 6866-6904 (2019). Reviewer: Piotr Biler (Wrocław) MSC: 35B40 35Q92 92C17 35K51 35B41 PDF BibTeX XML Cite \textit{J. Ahn}, J. Differ. Equations 266, No. 10, 6866--6904 (2019; Zbl 1415.35036) Full Text: DOI OpenURL
Lankeit, Elisa; Lankeit, Johannes Classical solutions to a logistic chemotaxis model with singular sensitivity and signal absorption. (English) Zbl 1414.35239 Nonlinear Anal., Real World Appl. 46, 421-445 (2019). Reviewer: Piotr Biler (Wrocław) MSC: 35Q92 35B40 PDF BibTeX XML Cite \textit{E. Lankeit} and \textit{J. Lankeit}, Nonlinear Anal., Real World Appl. 46, 421--445 (2019; Zbl 1414.35239) Full Text: DOI arXiv OpenURL
Mizukami, Masaaki The fast signal diffusion limit in a Keller-Segel system. (English) Zbl 1414.35242 J. Math. Anal. Appl. 472, No. 2, 1313-1330 (2019). Reviewer: Piotr Biler (Wrocław) MSC: 35Q92 35B30 92C17 PDF BibTeX XML Cite \textit{M. Mizukami}, J. Math. Anal. Appl. 472, No. 2, 1313--1330 (2019; Zbl 1414.35242) Full Text: DOI arXiv OpenURL
Khelghati, Ali; Baghaei, Khadijeh Boundedness of classical solutions for a chemotaxis system with general sensitivity function. (English) Zbl 07024360 Appl. Anal. 98, No. 3, 611-621 (2019). MSC: 35Kxx PDF BibTeX XML Cite \textit{A. Khelghati} and \textit{K. Baghaei}, Appl. Anal. 98, No. 3, 611--621 (2019; Zbl 07024360) Full Text: DOI OpenURL
Winkler, Michael A three-dimensional Keller-Segel-Navier-Stokes system with logistic source: global weak solutions and asymptotic stabilization. (English) Zbl 1408.35132 J. Funct. Anal. 276, No. 5, 1339-1401 (2019). MSC: 35Q30 35D30 35B40 35K55 92C17 35Q92 PDF BibTeX XML Cite \textit{M. Winkler}, J. Funct. Anal. 276, No. 5, 1339--1401 (2019; Zbl 1408.35132) Full Text: DOI OpenURL
Zheng, Pan; Mu, Chunlai; Willie, Robert; Hu, Xuegang Global asymptotic stability of steady states in a chemotaxis-growth system with singular sensitivity. (English) Zbl 1409.35103 Comput. Math. Appl. 75, No. 5, 1667-1675 (2018). MSC: 35K51 92C17 35B35 35B40 PDF BibTeX XML Cite \textit{P. Zheng} et al., Comput. Math. Appl. 75, No. 5, 1667--1675 (2018; Zbl 1409.35103) Full Text: DOI OpenURL
Black, Tobias; Lankeit, Johannes; Mizukami, Masaaki Singular sensitivity in a Keller-Segel-fluid system. (English) Zbl 1402.35006 J. Evol. Equ. 18, No. 2, 561-581 (2018). Reviewer: Piotr Biler (Wrocław) MSC: 35A01 35Q30 35Q92 92C17 35K51 PDF BibTeX XML Cite \textit{T. Black} et al., J. Evol. Equ. 18, No. 2, 561--581 (2018; Zbl 1402.35006) Full Text: DOI arXiv OpenURL
Winkler, Michael A critical blow-up exponent in a chemotaxis system with nonlinear signal production. (English) Zbl 1391.35240 Nonlinearity 31, No. 5, 2031-2056 (2018). MSC: 35K65 35Q92 35B44 35B33 92C17 PDF BibTeX XML Cite \textit{M. Winkler}, Nonlinearity 31, No. 5, 2031--2056 (2018; Zbl 1391.35240) Full Text: DOI Link OpenURL
Fujie, Kentarou; Senba, Takasi A sufficient condition of sensitivity functions for boundedness of solutions to a parabolic-parabolic chemotaxis system. (English) Zbl 1397.35122 Nonlinearity 31, No. 4, 1639-1672 (2018). Reviewer: Andrey Zahariev (Plovdiv) MSC: 35K45 35B45 35Q92 92C17 PDF BibTeX XML Cite \textit{K. Fujie} and \textit{T. Senba}, Nonlinearity 31, No. 4, 1639--1672 (2018; Zbl 1397.35122) Full Text: DOI OpenURL
Winkler, Michael; Yokota, Tomomi Stabilization in the logarithmic Keller-Segel system. (English) Zbl 1391.35066 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 170, 123-141 (2018). MSC: 35B40 35K65 92C17 35K51 PDF BibTeX XML Cite \textit{M. Winkler} and \textit{T. Yokota}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 170, 123--141 (2018; Zbl 1391.35066) Full Text: DOI OpenURL
Ding, Mengyao Global boundedness in a fully parabolic quasilinear chemotaxis system with singular sensitivity. (English) Zbl 1429.35038 J. Math. Anal. Appl. 461, No. 2, 1260-1270 (2018). Reviewer: Yuanyuan Ke (Beijing) MSC: 35B45 35K51 35B44 92C17 35K59 35Q92 PDF BibTeX XML Cite \textit{M. Ding}, J. Math. Anal. Appl. 461, No. 2, 1260--1270 (2018; Zbl 1429.35038) Full Text: DOI OpenURL
Winkler, Michael Renormalized radial large-data solutions to the higher-dimensional Keller-Segel system with singular sensitivity and signal absorption. (English) Zbl 1378.35165 J. Differ. Equations 264, No. 3, 2310-2350 (2018). MSC: 35K55 35D30 35B65 92C17 35Q92 PDF BibTeX XML Cite \textit{M. Winkler}, J. Differ. Equations 264, No. 3, 2310--2350 (2018; Zbl 1378.35165) Full Text: DOI OpenURL
Lankeit, Johannes; Winkler, Michael A generalized solution concept for the Keller-Segel system with logarithmic sensitivity: global solvability for large nonradial data. (English) Zbl 1373.35166 NoDEA, Nonlinear Differ. Equ. Appl. 24, No. 4, Paper No. 49, 33 p. (2017). MSC: 35K55 35D99 92C17 PDF BibTeX XML Cite \textit{J. Lankeit} and \textit{M. Winkler}, NoDEA, Nonlinear Differ. Equ. Appl. 24, No. 4, Paper No. 49, 33 p. (2017; Zbl 1373.35166) Full Text: DOI arXiv OpenURL
Lee, Seongwon; Kim, Se-woong; Oh, Youngmin; Hwang, Hyung Ju Mathematical modeling and its analysis for instability of the immune system induced by chemotaxis. (English) Zbl 1378.35314 J. Math. Biol. 75, No. 5, 1101-1131 (2017). Reviewer: Anthony D. Osborne (Keele) MSC: 35Q92 92C45 92C17 65M08 35B35 35K57 PDF BibTeX XML Cite \textit{S. Lee} et al., J. Math. Biol. 75, No. 5, 1101--1131 (2017; Zbl 1378.35314) Full Text: DOI OpenURL
Wang, Wei; Li, Yan; Yu, Hao Global boundedness in higher dimensions for a fully parabolic chemotaxis system with singular sensitivity. (English) Zbl 1371.35007 Discrete Contin. Dyn. Syst., Ser. B 22, No. 10, 3663-3669 (2017). MSC: 35B35 35B40 35K55 92C17 PDF BibTeX XML Cite \textit{W. Wang} et al., Discrete Contin. Dyn. Syst., Ser. B 22, No. 10, 3663--3669 (2017; Zbl 1371.35007) Full Text: DOI OpenURL
Fan, Jishan; Liu, Dan; Samet, Bessem; Zhou, Yong A regularity criterion for the Keller-Segel-Euler system. (English) Zbl 1404.35351 Bound. Value Probl. 2017, Paper No. 124, 7 p. (2017). MSC: 35Q35 35B65 35D35 PDF BibTeX XML Cite \textit{J. Fan} et al., Bound. Value Probl. 2017, Paper No. 124, 7 p. (2017; Zbl 1404.35351) Full Text: DOI OpenURL
Tao, Youshan; Winkler, Michael Effects of signal-dependent motilities in a Keller-Segel-type reaction-diffusion system. (English) Zbl 06761738 Math. Models Methods Appl. Sci. 27, No. 9, 1645-1683 (2017). MSC: 35A01 35B40 35B65 35K55 35Q92 92C17 PDF BibTeX XML Cite \textit{Y. Tao} and \textit{M. Winkler}, Math. Models Methods Appl. Sci. 27, No. 9, 1645--1683 (2017; Zbl 06761738) Full Text: DOI OpenURL
Bellomo, Nicola; Winkler, Michael Finite-time blow-up in a degenerate chemotaxis system with flux limitation. (English) Zbl 1367.35044 Trans. Am. Math. Soc., Ser. B 4, 31-67 (2017). MSC: 35B44 35K65 35K20 35Q92 92C17 PDF BibTeX XML Cite \textit{N. Bellomo} and \textit{M. Winkler}, Trans. Am. Math. Soc., Ser. B 4, 31--67 (2017; Zbl 1367.35044) Full Text: DOI OpenURL
Zhao, Xiangdong; Zheng, Sining Global boundedness to a chemotaxis system with singular sensitivity and logistic source. (English) Zbl 1371.35151 Z. Angew. Math. Phys. 68, No. 1, Paper No. 2, 13 p. (2017). MSC: 35K55 35B45 35B40 92C17 35K40 PDF BibTeX XML Cite \textit{X. Zhao} and \textit{S. Zheng}, Z. Angew. Math. Phys. 68, No. 1, Paper No. 2, 13 p. (2017; Zbl 1371.35151) Full Text: DOI OpenURL
Wang, Wei; Ding, Mengyao; Li, Yan Global boundedness in a quasilinear chemotaxis system with general density-signal governed sensitivity. (English) Zbl 1367.35039 J. Differ. Equations 263, No. 5, 2851-2873 (2017). MSC: 35B40 35B35 35K55 92C17 PDF BibTeX XML Cite \textit{W. Wang} et al., J. Differ. Equations 263, No. 5, 2851--2873 (2017; Zbl 1367.35039) Full Text: DOI OpenURL
Lankeit, Johannes Locally bounded global solutions to a chemotaxis consumption model with singular sensitivity and nonlinear diffusion. (English) Zbl 1359.35103 J. Differ. Equations 262, No. 7, 4052-4084 (2017). MSC: 35K59 35Q92 35A01 35K65 92C17 PDF BibTeX XML Cite \textit{J. Lankeit}, J. Differ. Equations 262, No. 7, 4052--4084 (2017; Zbl 1359.35103) Full Text: DOI arXiv OpenURL
Galakhov, Evgeny; Salieva, Olga; Tello, J. Ignacio On a parabolic-elliptic system with chemotaxis and logistic type growth. (English) Zbl 1347.35090 J. Differ. Equations 261, No. 8, 4631-4647 (2016). MSC: 35G31 92C17 35B40 35B35 PDF BibTeX XML Cite \textit{E. Galakhov} et al., J. Differ. Equations 261, No. 8, 4631--4647 (2016; Zbl 1347.35090) Full Text: DOI OpenURL
Zhao, Xiangdong; Zheng, Sining Global boundedness of solutions in a parabolic-parabolic chemotaxis system with singular sensitivity. (English) Zbl 1381.35081 J. Math. Anal. Appl. 443, No. 1, 445-452 (2016). MSC: 35K51 35Q92 35A09 92C17 PDF BibTeX XML Cite \textit{X. Zhao} and \textit{S. Zheng}, J. Math. Anal. Appl. 443, No. 1, 445--452 (2016; Zbl 1381.35081) Full Text: DOI arXiv OpenURL
Wu, Sainan; Wu, Boying Global boundedness in a quasilinear attraction-repulsion chemotaxis model with nonlinear sensitivity. (English) Zbl 1339.35068 J. Math. Anal. Appl. 442, No. 2, 554-582 (2016). MSC: 35B45 35K51 92C17 35K58 PDF BibTeX XML Cite \textit{S. Wu} and \textit{B. Wu}, J. Math. Anal. Appl. 442, No. 2, 554--582 (2016; Zbl 1339.35068) Full Text: DOI OpenURL
Winkler, Michael The two-dimensional Keller-Segel system with singular sensitivity and signal absorption: global large-data solutions and their relaxation properties. (English) Zbl 1383.35099 Math. Models Methods Appl. Sci. 26, No. 5, 987-1024 (2016). MSC: 35K40 35Q92 92C17 35B40 35B65 35D30 35K59 35K55 PDF BibTeX XML Cite \textit{M. Winkler}, Math. Models Methods Appl. Sci. 26, No. 5, 987--1024 (2016; Zbl 1383.35099) Full Text: DOI OpenURL
Li, Yan; Li, Yuxiang Blow-up of nonradial solutions to attraction-repulsion chemotaxis system in two dimensions. (English) Zbl 1381.35109 Nonlinear Anal., Real World Appl. 30, 170-183 (2016). MSC: 35M33 35B44 35Q92 92C17 PDF BibTeX XML Cite \textit{Y. Li} and \textit{Y. Li}, Nonlinear Anal., Real World Appl. 30, 170--183 (2016; Zbl 1381.35109) Full Text: DOI OpenURL
Lankeit, Johannes A new approach toward boundedness in a two-dimensional parabolic chemotaxis system with singular sensitivity. (English) Zbl 1333.35100 Math. Methods Appl. Sci. 39, No. 3, 394-404 (2016). MSC: 35K55 35A01 92C17 35Q92 35B65 PDF BibTeX XML Cite \textit{J. Lankeit}, Math. Methods Appl. Sci. 39, No. 3, 394--404 (2016; Zbl 1333.35100) Full Text: DOI arXiv OpenURL
Cao, Junhong; Wang, Wei; Yu, Hao Asymptotic behavior of solutions to two-dimensional chemotaxis system with logistic source and singular sensitivity. (English) Zbl 1331.35047 J. Math. Anal. Appl. 436, No. 1, 382-392 (2016). MSC: 35B40 92C17 PDF BibTeX XML Cite \textit{J. Cao} et al., J. Math. Anal. Appl. 436, No. 1, 382--392 (2016; Zbl 1331.35047) Full Text: DOI OpenURL
Senba, Takasi; Fujie, Kentarou Global existence and boundedness in a parabolic-elliptic Keller-Segel system with general sensitivity. (English) Zbl 1330.35051 Discrete Contin. Dyn. Syst., Ser. B 21, No. 1, 81-102 (2016). MSC: 35B45 35K55 92C17 PDF BibTeX XML Cite \textit{T. Senba} and \textit{K. Fujie}, Discrete Contin. Dyn. Syst., Ser. B 21, No. 1, 81--102 (2016; Zbl 1330.35051) Full Text: DOI OpenURL
Li, Yuhuan; Lin, Ke; Mu, Chunlai Boundedness and asymptotic behavior of solutions to a chemotaxis-haptotaxis model in high dimensions. (English) Zbl 1328.35075 Appl. Math. Lett. 50, 91-97 (2015). MSC: 35K51 92C17 35Q92 35B40 PDF BibTeX XML Cite \textit{Y. Li} et al., Appl. Math. Lett. 50, 91--97 (2015; Zbl 1328.35075) Full Text: DOI OpenURL
Zheng, Pan; Mu, Chunlai; Hu, Xuegang; Zhang, Qinghua Global boundedness in a quasilinear chemotaxis system with signal-dependent sensitivity. (English) Zbl 06440060 J. Math. Anal. Appl. 428, No. 1, 508-524 (2015). MSC: 35-XX 34-XX PDF BibTeX XML Cite \textit{P. Zheng} et al., J. Math. Anal. Appl. 428, No. 1, 508--524 (2015; Zbl 06440060) Full Text: DOI OpenURL
Fujie, Kentarou; Winkler, Michael; Yokota, Tomomi Boundedness of solutions to parabolic-elliptic Keller-Segel systems with signal-dependent sensitivity. (English) Zbl 1329.35011 Math. Methods Appl. Sci. 38, No. 6, 1212-1224 (2015). Reviewer: Christian Stinner (München) MSC: 35A09 35A01 35K55 92C17 35K59 PDF BibTeX XML Cite \textit{K. Fujie} et al., Math. Methods Appl. Sci. 38, No. 6, 1212--1224 (2015; Zbl 1329.35011) Full Text: DOI OpenURL
Wang, Qi Global solutions of a Keller-Segel system with saturated logarithmic sensitivity function. (English) Zbl 1335.92015 Commun. Pure Appl. Anal. 14, No. 2, 383-396 (2015). Reviewer: Piotr Biler (Wroclaw) MSC: 92C17 35Q92 35K55 35B40 PDF BibTeX XML Cite \textit{Q. Wang}, Commun. Pure Appl. Anal. 14, No. 2, 383--396 (2015; Zbl 1335.92015) Full Text: DOI arXiv OpenURL
Wang, Qi Boundary spikes of a Keller-Segel chemotaxis system with saturated logarithmic sensitivity. (English) Zbl 1325.92019 Discrete Contin. Dyn. Syst., Ser. B 20, No. 4, 1231-1250 (2015). MSC: 92C17 35K51 35K57 PDF BibTeX XML Cite \textit{Q. Wang}, Discrete Contin. Dyn. Syst., Ser. B 20, No. 4, 1231--1250 (2015; Zbl 1325.92019) Full Text: DOI arXiv OpenURL
Fujie, Kentarou Boundedness in a fully parabolic chemotaxis system with singular sensitivity. (English) Zbl 1310.35144 J. Math. Anal. Appl. 424, No. 1, 675-684 (2015). MSC: 35K51 92C17 35K58 PDF BibTeX XML Cite \textit{K. Fujie}, J. Math. Anal. Appl. 424, No. 1, 675--684 (2015; Zbl 1310.35144) Full Text: DOI OpenURL
Peng, Hongyun; Wen, Huanyao; Zhu, Changjiang Global well-posedness and zero diffusion limit of classical solutions to 3D conservation laws arising in chemotaxis. (English) Zbl 1305.92022 Z. Angew. Math. Phys. 65, No. 6, 1167-1188 (2014). MSC: 92C17 35M99 35Q99 35L65 PDF BibTeX XML Cite \textit{H. Peng} et al., Z. Angew. Math. Phys. 65, No. 6, 1167--1188 (2014; Zbl 1305.92022) Full Text: DOI arXiv OpenURL
Fujie, Kentarou; Winkler, Michael; Yokota, Tomomi Blow-up prevention by logistic sources in a parabolic-elliptic Keller-Segel system with singular sensitivity. (English) Zbl 1297.35051 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 109, 56-71 (2014). MSC: 35B44 35K59 35B35 35B45 92C17 PDF BibTeX XML Cite \textit{K. Fujie} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 109, 56--71 (2014; Zbl 1297.35051) Full Text: DOI OpenURL
Carrillo, José Antonio; Lisini, Stefano; Mainini, Edoardo Uniqueness for Keller-Segel-type chemotaxis models. (English) Zbl 1277.35009 Discrete Contin. Dyn. Syst. 34, No. 4, 1319-1338 (2014). MSC: 35A02 35K45 35Q92 35K59 PDF BibTeX XML Cite \textit{J. A. Carrillo} et al., Discrete Contin. Dyn. Syst. 34, No. 4, 1319--1338 (2014; Zbl 1277.35009) Full Text: DOI arXiv OpenURL
Rodríguez, N. On the global well-posedness theory for a class of PDE models for criminal activity. (English) Zbl 1286.91110 Physica D 260, 191-200 (2013). MSC: 91D10 35Q91 35K51 PDF BibTeX XML Cite \textit{N. Rodríguez}, Physica D 260, 191--200 (2013; Zbl 1286.91110) Full Text: DOI OpenURL
Fan, Jishan; Zhao, Kun Blow up criterion for a hyperbolic-parabolic system arising from chemotaxis. (English) Zbl 1252.35088 J. Math. Anal. Appl. 394, No. 2, 687-695 (2012). MSC: 35B44 92C17 PDF BibTeX XML Cite \textit{J. Fan} and \textit{K. Zhao}, J. Math. Anal. Appl. 394, No. 2, 687--695 (2012; Zbl 1252.35088) Full Text: DOI OpenURL
Perthame, Benoît Mathematical models of cell self-organization. (English) Zbl 1248.35214 J. Egypt. Math. Soc. 19, No. 1-2, 52-56 (2011). MSC: 35Q92 92C37 35K57 92C17 PDF BibTeX XML Cite \textit{B. Perthame}, J. Egypt. Math. Soc. 19, No. 1--2, 52--56 (2011; Zbl 1248.35214) Full Text: DOI OpenURL
Stinner, Christian; Winkler, Michael Global weak solutions in a chemotaxis system with large singular sensitivity. (English) Zbl 1268.35072 Nonlinear Anal., Real World Appl. 12, No. 6, 3727-3740 (2011). MSC: 35K51 92C17 35Q92 35A20 PDF BibTeX XML Cite \textit{C. Stinner} and \textit{M. Winkler}, Nonlinear Anal., Real World Appl. 12, No. 6, 3727--3740 (2011; Zbl 1268.35072) Full Text: DOI OpenURL
Winkler, Michael Global solutions in a fully parabolic chemotaxis system with singular sensitivity. (English) Zbl 1291.92018 Math. Methods Appl. Sci. 34, No. 2, 176-190 (2011). MSC: 92C17 35K55 35B35 35B40 PDF BibTeX XML Cite \textit{M. Winkler}, Math. Methods Appl. Sci. 34, No. 2, 176--190 (2011; Zbl 1291.92018) Full Text: DOI OpenURL
Winkler, Michael Absence of collapse in a parabolic chemotaxis system with signal-dependent sensitivity. (English) Zbl 1205.35037 Math. Nachr. 283, No. 11, 1664-1673 (2010). Reviewer: Philippe Laurençot (Toulouse) MSC: 35B45 35K51 92C17 35K58 PDF BibTeX XML Cite \textit{M. Winkler}, Math. Nachr. 283, No. 11, 1664--1673 (2010; Zbl 1205.35037) Full Text: DOI OpenURL
Guo, Yan; Hwang, Hyung Ju Pattern formation. I: The Keller-Segel model. (English) Zbl 1213.35087 J. Differ. Equations 249, No. 7, 1519-1530 (2010). Reviewer: Sebastian Anita (Iaşi) MSC: 35B36 92C15 92C17 PDF BibTeX XML Cite \textit{Y. Guo} and \textit{H. J. Hwang}, J. Differ. Equations 249, No. 7, 1519--1530 (2010; Zbl 1213.35087) Full Text: DOI arXiv OpenURL
Winkler, Michael Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model. (English) Zbl 1190.92004 J. Differ. Equations 248, No. 12, 2889-2905 (2010). MSC: 92C17 35B40 35K35 35K55 35B35 35Q92 PDF BibTeX XML Cite \textit{M. Winkler}, J. Differ. Equations 248, No. 12, 2889--2905 (2010; Zbl 1190.92004) Full Text: DOI OpenURL
Hillen, T.; Painter, K. J. A user’s guide to PDE models for chemotaxis. (English) Zbl 1161.92003 J. Math. Biol. 58, No. 1-2, 183-217 (2009). MSC: 92C17 35Q92 65C20 PDF BibTeX XML Cite \textit{T. Hillen} and \textit{K. J. Painter}, J. Math. Biol. 58, No. 1--2, 183--217 (2009; Zbl 1161.92003) Full Text: DOI OpenURL
Calvez, Vincent; Carrillo, José A. Volume effects in the Keller–Segel model: energy estimates preventing blow-up. (English) Zbl 1116.35057 J. Math. Pures Appl. (9) 86, No. 2, 155-175 (2006). Reviewer: Philippe Laurençot (Toulouse) MSC: 35K55 35K50 35B45 92C17 PDF BibTeX XML Cite \textit{V. Calvez} and \textit{J. A. Carrillo}, J. Math. Pures Appl. (9) 86, No. 2, 155--175 (2006; Zbl 1116.35057) Full Text: DOI OpenURL
Calvez, V.; Perthame, B. A Lyapunov function for a two-chemical species version of the chemotaxis model. (English) Zbl 1103.35034 BIT 46, Suppl., S85-S97 (2006). MSC: 35K50 35B45 35Q80 92C17 PDF BibTeX XML Cite \textit{V. Calvez} and \textit{B. Perthame}, BIT 46, S85--S97 (2006; Zbl 1103.35034) Full Text: DOI OpenURL
Senba, Takasi; Suzuki, Takasi A quasi-linear parabolic system of chemotaxis. (English) Zbl 1134.35059 Abstr. Appl. Anal. 2006, Article ID 23061, 21 p. (2006). MSC: 35K50 35K55 35B40 92C17 PDF BibTeX XML Cite \textit{T. Senba} and \textit{T. Suzuki}, Abstr. Appl. Anal. 2006, Article ID 23061, 21 p. (2006; Zbl 1134.35059) Full Text: DOI EuDML OpenURL
Aida, Masashi; Osaki, Koichi; Tsujikawa, Tohru; Yagi, Atsushi; Mimura, Masayasu Chemotaxis and growth system with singular sensitivity function. (English) Zbl 1066.92004 Nonlinear Anal., Real World Appl. 6, No. 2, 323-336 (2005). MSC: 92C17 35K15 35B40 35Q92 PDF BibTeX XML Cite \textit{M. Aida} et al., Nonlinear Anal., Real World Appl. 6, No. 2, 323--336 (2005; Zbl 1066.92004) Full Text: DOI Link OpenURL
Kowalczyk, R. Preventing blow up in a chemotaxis model. (English) Zbl 1065.35063 J. Math. Anal. Appl. 305, No. 2, 566-588 (2005). Reviewer: Messoud A. Efendiev (Berlin) MSC: 35B40 92C17 35K57 35B45 PDF BibTeX XML Cite \textit{R. Kowalczyk}, J. Math. Anal. Appl. 305, No. 2, 566--588 (2005; Zbl 1065.35063) Full Text: DOI OpenURL
Perthame, Benoît PDE models for chemotactic movements: parabolic, hyperbolic and kinetic. (English) Zbl 1099.35157 Appl. Math., Praha 49, No. 6, 539-564 (2004). MSC: 35Q80 35B40 92C17 35K65 35D05 PDF BibTeX XML Cite \textit{B. Perthame}, Appl. Math., Praha 49, No. 6, 539--564 (2004; Zbl 1099.35157) Full Text: DOI EuDML OpenURL
Hillen, T.; Painter, K. Global existence for a parabolic chemotaxis model with prevention of overcrowding. (English) Zbl 0998.92006 Adv. Appl. Math. 26, No. 4, 280-301 (2001). MSC: 92C17 35K50 35K25 65C20 PDF BibTeX XML Cite \textit{T. Hillen} and \textit{K. Painter}, Adv. Appl. Math. 26, No. 4, 280--301 (2001; Zbl 0998.92006) Full Text: DOI Link OpenURL
Boy-Dalverny, A.; Madaune-Tort, M. Global solutions in tree dimensions for systems describing a chemotaxis phenomenon. (English) Zbl 1017.92005 Adv. Appl. Math. 26, No. 1, 63-88 (2001). MSC: 92C17 35Q92 35A05 PDF BibTeX XML Cite \textit{A. Boy-Dalverny} and \textit{M. Madaune-Tort}, Adv. Appl. Math. 26, No. 1, 63--88 (2001; Zbl 1017.92005) Full Text: DOI OpenURL