Wang, Chang-Jian; Zheng, Zi-Han The effects of cross-diffusion and logistic source on the boundedness of solutions to a pursuit-evasion model. (English) Zbl 07804292 Electron. Res. Arch. 31, No. 6, 3362-3380 (2023). MSC: 35A09 35B40 35K51 35K59 92C17 PDFBibTeX XMLCite \textit{C.-J. Wang} and \textit{Z.-H. Zheng}, Electron. Res. Arch. 31, No. 6, 3362--3380 (2023; Zbl 07804292) Full Text: DOI
Tang, Haotian; Zheng, Jiashan; Li, Kaiqiang Global and bounded solution to a quasilinear parabolic-elliptic pursuit-evasion system in \(N\)-dimensional domains. (English) Zbl 1518.35116 J. Math. Anal. Appl. 527, No. 1, Part 2, Article ID 127406, 18 p. (2023). MSC: 35B40 35K51 35K59 92C17 PDFBibTeX XMLCite \textit{H. Tang} et al., J. Math. Anal. Appl. 527, No. 1, Part 2, Article ID 127406, 18 p. (2023; Zbl 1518.35116) Full Text: DOI
Liu, Xu; Zheng, Jiashan Convergence rates of solutions in a predator-prey system with indirect pursuit-evasion interaction in domains of arbitrary dimension. (English) Zbl 1502.35019 Discrete Contin. Dyn. Syst., Ser. B 28, No. 3, 2269-2293 (2023). MSC: 35B40 35K51 35K59 92C17 PDFBibTeX XMLCite \textit{X. Liu} and \textit{J. Zheng}, Discrete Contin. Dyn. Syst., Ser. B 28, No. 3, 2269--2293 (2023; Zbl 1502.35019) Full Text: DOI
Zheng, Jiashan; Zhang, Pengmei Blow-up prevention by logistic source an N-dimensional parabolic-elliptic predator-prey system with indirect pursuit-evasion interaction. (English) Zbl 1501.35095 J. Math. Anal. Appl. 519, No. 1, Article ID 126741, 12 p. (2023). MSC: 35B44 35K51 35K57 92D25 PDFBibTeX XMLCite \textit{J. Zheng} and \textit{P. Zhang}, J. Math. Anal. Appl. 519, No. 1, Article ID 126741, 12 p. (2023; Zbl 1501.35095) Full Text: DOI
Qi, Dayong; Ke, Yuanyuan Large time behavior in a predator-prey system with pursuit-evasion interaction. (English) Zbl 1500.35047 Discrete Contin. Dyn. Syst., Ser. B 27, No. 8, 4531-4549 (2022). MSC: 35B40 35B65 35K51 35K59 92C17 PDFBibTeX XMLCite \textit{D. Qi} and \textit{Y. Ke}, Discrete Contin. Dyn. Syst., Ser. B 27, No. 8, 4531--4549 (2022; Zbl 1500.35047) Full Text: DOI
Qiu, Shuyan; Mu, Chunlai; Yi, Hong Boundedness and asymptotic stability in a predator-prey chemotaxis system with indirect pursuit-evasion dynamics. (English) Zbl 1513.35295 Acta Math. Sci., Ser. B, Engl. Ed. 42, No. 3, 1035-1057 (2022). MSC: 35K35 35K55 35B35 92C17 PDFBibTeX XMLCite \textit{S. Qiu} et al., Acta Math. Sci., Ser. B, Engl. Ed. 42, No. 3, 1035--1057 (2022; Zbl 1513.35295) Full Text: DOI
Bellomo, N.; Outada, N.; Soler, J.; Tao, Y.; Winkler, M. Chemotaxis and cross-diffusion models in complex environments: models and analytic problems toward a multiscale vision. (English) Zbl 1497.35039 Math. Models Methods Appl. Sci. 32, No. 4, 713-792 (2022). Reviewer: Lingeshwaran Shangerganesh (Ponda) MSC: 35B36 35B40 35B44 35K51 35K57 35Q35 92C17 91D10 PDFBibTeX XMLCite \textit{N. Bellomo} et al., Math. Models Methods Appl. Sci. 32, No. 4, 713--792 (2022; Zbl 1497.35039) Full Text: DOI
Telch, Bruno A parabolic-quasilinear predator-prey model under pursuit-evasion dynamics. (English) Zbl 1491.35005 J. Math. Anal. Appl. 514, No. 1, Article ID 126276, 14 p. (2022). MSC: 35A01 35K51 35K59 92C17 92D25 PDFBibTeX XMLCite \textit{B. Telch}, J. Math. Anal. Appl. 514, No. 1, Article ID 126276, 14 p. (2022; Zbl 1491.35005) Full Text: DOI
Corbin, Gregor; Klar, Axel; Surulescu, Christina; Engwer, Christian; Wenske, Michael; Nieto, Juanjo; Soler, Juan Modeling glioma invasion with anisotropy- and hypoxia-triggered motility enhancement: from subcellular dynamics to macroscopic PDEs with multiple taxis. (English) Zbl 1473.92007 Math. Models Methods Appl. Sci. 31, No. 1, 177-222 (2021). MSC: 92-10 92C17 35Q92 PDFBibTeX XMLCite \textit{G. Corbin} et al., Math. Models Methods Appl. Sci. 31, No. 1, 177--222 (2021; Zbl 1473.92007) Full Text: DOI arXiv
López, José Luis A quantum approach to Keller-Segel dynamics via a dissipative nonlinear Schrödinger equation. (English) Zbl 1465.35273 Discrete Contin. Dyn. Syst. 41, No. 6, 2601-2617 (2021). MSC: 35K40 35K59 35Q55 92C17 PDFBibTeX XMLCite \textit{J. L. López}, Discrete Contin. Dyn. Syst. 41, No. 6, 2601--2617 (2021; Zbl 1465.35273) Full Text: DOI
Kolbe, Niklas; Sfakianakis, Nikolaos; Stinner, Christian; Surulescu, Christina; Lenz, Jonas Modeling multiple taxis: tumor invasion with phenotypic heterogeneity, haptotaxis, and unilateral interspecies repellence. (English) Zbl 1467.35323 Discrete Contin. Dyn. Syst., Ser. B 26, No. 1, 443-481 (2021). Reviewer: Yaroslav Baranetskij (Lviv) MSC: 35Q92 92C17 92C37 35K55 35A01 35D30 92-08 PDFBibTeX XMLCite \textit{N. Kolbe} et al., Discrete Contin. Dyn. Syst., Ser. B 26, No. 1, 443--481 (2021; Zbl 1467.35323) Full Text: DOI arXiv
Telch, Bruno Global boundedness in a chemotaxis quasilinear parabolic predator-prey system with pursuit-evasion. (English) Zbl 1464.35145 Nonlinear Anal., Real World Appl. 59, Article ID 103269, 12 p. (2021). MSC: 35K51 35K59 92C17 92D25 35B45 PDFBibTeX XMLCite \textit{B. Telch}, Nonlinear Anal., Real World Appl. 59, Article ID 103269, 12 p. (2021; Zbl 1464.35145) Full Text: DOI
Amorim, Paulo; Telch, Bruno A chemotaxis predator-prey model with indirect pursuit-evasion dynamics and parabolic signal. (English) Zbl 1470.35177 J. Math. Anal. Appl. 500, No. 1, Article ID 125128, 27 p. (2021). Reviewer: Takashi Suzuki (Osaka) MSC: 35K51 35K59 92D25 35K57 92C17 PDFBibTeX XMLCite \textit{P. Amorim} and \textit{B. Telch}, J. Math. Anal. Appl. 500, No. 1, Article ID 125128, 27 p. (2021; Zbl 1470.35177) Full Text: DOI
Ahn, Jaewook; Lee, Jihoon Asymptotics of chemotaxis systems with fractional dissipation for small data in critical Sobolev space. (English) Zbl 1462.35065 Acta Appl. Math. 169, 199-215 (2020). MSC: 35B40 35R11 35K15 92C17 PDFBibTeX XMLCite \textit{J. Ahn} and \textit{J. Lee}, Acta Appl. Math. 169, 199--215 (2020; Zbl 1462.35065) Full Text: DOI
Fuest, Mario Global solutions near homogeneous steady states in a multidimensional population model with both predator- and prey-taxis. (English) Zbl 1458.35222 SIAM J. Math. Anal. 52, No. 6, 5865-5891 (2020). Reviewer: Thomas Giletti (Vandœuvre-lès-Nancy) MSC: 35K57 35B35 35K55 92D25 PDFBibTeX XMLCite \textit{M. Fuest}, SIAM J. Math. Anal. 52, No. 6, 5865--5891 (2020; Zbl 1458.35222) Full Text: DOI arXiv
Li, Genglin; Tao, Youshan; Winkler, Michael Large time behavior in a predator-prey system with indirect pursuit-evasion interaction. (English) Zbl 1453.92250 Discrete Contin. Dyn. Syst., Ser. B 25, No. 11, 4383-4396 (2020). MSC: 92D25 92C17 35Q92 PDFBibTeX XMLCite \textit{G. Li} et al., Discrete Contin. Dyn. Syst., Ser. B 25, No. 11, 4383--4396 (2020; Zbl 1453.92250) Full Text: DOI
Bellomo, N.; Tao, Y.; Winkler, M. Chemotaxis systems in complex frameworks: pattern formation, qualitative analysis and blowup prevention. (English) Zbl 1451.92062 Math. Models Methods Appl. Sci. 30, No. 6, 1033-1039 (2020). MSC: 92C17 35Q92 PDFBibTeX XMLCite \textit{N. Bellomo} et al., Math. Models Methods Appl. Sci. 30, No. 6, 1033--1039 (2020; Zbl 1451.92062) Full Text: DOI
Burczak, Jan; Granero-Belinchón, Rafael Boundedness and homogeneous asymptotics for a fractional logistic Keller-Segel equations. (English) Zbl 1439.35054 Discrete Contin. Dyn. Syst., Ser. S 13, No. 2, 139-164 (2020). MSC: 35B40 35B65 35K51 35R11 92C17 35A01 35S10 PDFBibTeX XMLCite \textit{J. Burczak} and \textit{R. Granero-Belinchón}, Discrete Contin. Dyn. Syst., Ser. S 13, No. 2, 139--164 (2020; Zbl 1439.35054) Full Text: DOI arXiv
Amorim, Paulo; Telch, Bruno; Villada, Luis M. A reaction-diffusion predator-prey model with pursuit, evasion, and nonlocal sensing. (English) Zbl 1497.92190 Math. Biosci. Eng. 16, No. 5, 5114-5145 (2019). MSC: 92D25 35K57 92C17 35Q92 PDFBibTeX XMLCite \textit{P. Amorim} et al., Math. Biosci. Eng. 16, No. 5, 5114--5145 (2019; Zbl 1497.92190) Full Text: DOI
Burini, D.; Chouhad, N. A multiscale view of nonlinear diffusion in biology: from cells to tissues. (English) Zbl 1427.35291 Math. Models Methods Appl. Sci. 29, No. 4, 791-823 (2019). MSC: 35Q92 92C17 82C40 PDFBibTeX XMLCite \textit{D. Burini} and \textit{N. Chouhad}, Math. Models Methods Appl. Sci. 29, No. 4, 791--823 (2019; Zbl 1427.35291) Full Text: DOI
Estrada-Rodriguez, Gissell; Gimperlein, Heiko; Painter, Kevin J.; Stocek, Jakub Space-time fractional diffusion in cell movement models with delay. (English) Zbl 1411.92036 Math. Models Methods Appl. Sci. 29, No. 1, 65-88 (2019). MSC: 92C17 35K40 35Q92 35R11 PDFBibTeX XMLCite \textit{G. Estrada-Rodriguez} et al., Math. Models Methods Appl. Sci. 29, No. 1, 65--88 (2019; Zbl 1411.92036) Full Text: DOI arXiv
Bellomo, N.; Tao, Y.; Winkler, M. Cross-diffusion models: analytic and multiscale problems. (English) Zbl 1408.35078 Math. Models Methods Appl. Sci. 28, No. 11, 2097-2102 (2018). MSC: 35K57 35J57 35K51 35Q92 92D25 PDFBibTeX XMLCite \textit{N. Bellomo} et al., Math. Models Methods Appl. Sci. 28, No. 11, 2097--2102 (2018; Zbl 1408.35078) Full Text: DOI
Perthame, Benoît; Sun, Weiran; Tang, Min The fractional diffusion limit of a kinetic model with biochemical pathway. (English) Zbl 1395.35015 Z. Angew. Math. Phys. 69, No. 3, Paper No. 67, 15 p. (2018). MSC: 35B25 35R11 82C40 92C17 35Q92 PDFBibTeX XMLCite \textit{B. Perthame} et al., Z. Angew. Math. Phys. 69, No. 3, Paper No. 67, 15 p. (2018; Zbl 1395.35015) Full Text: DOI arXiv
Estrada-Rodriguez, Gissell; Gimperlein, Heiko; Painter, Kevin J. Fractional Patlak-Keller-Segel equations for chemotactic superdiffusion. (English) Zbl 1390.92024 SIAM J. Appl. Math. 78, No. 2, 1155-1173 (2018). MSC: 92C17 35R11 35Q92 PDFBibTeX XMLCite \textit{G. Estrada-Rodriguez} et al., SIAM J. Appl. Math. 78, No. 2, 1155--1173 (2018; Zbl 1390.92024) Full Text: DOI arXiv
Bellomo, N.; Bellouquid, A.; Chouhad, N. From a multiscale derivation of nonlinear cross-diffusion models to Keller-Segel models in a Navier-Stokes fluid. (English) Zbl 1353.35038 Math. Models Methods Appl. Sci. 26, No. 11, 2041-2069 (2016). MSC: 35B27 35A01 35B40 35K55 35K57 35Q30 35K40 92C17 PDFBibTeX XMLCite \textit{N. Bellomo} et al., Math. Models Methods Appl. Sci. 26, No. 11, 2041--2069 (2016; Zbl 1353.35038) Full Text: DOI
Bellomo, N.; Brezzi, F. Mathematics, complexity and multiscale features of large systems of self-propelled particles. (English) Zbl 1398.92024 Math. Models Methods Appl. Sci. 26, No. 2, 207-214 (2016). MSC: 92C10 35Q92 PDFBibTeX XMLCite \textit{N. Bellomo} and \textit{F. Brezzi}, Math. Models Methods Appl. Sci. 26, No. 2, 207--214 (2016; Zbl 1398.92024) Full Text: DOI