Kong, Fanze; Wei, Juncheng; Xu, Liangshun The existence and stability of spikes in the one-dimensional Keller-Segel model with logistic growth. (English) Zbl 1505.35021 J. Math. Biol. 86, No. 1, Paper No. 6, 54 p. (2023). MSC: 35B25 35B40 35K51 35K59 92C17 PDF BibTeX XML Cite \textit{F. Kong} et al., J. Math. Biol. 86, No. 1, Paper No. 6, 54 p. (2023; Zbl 1505.35021) Full Text: DOI OpenURL
Fujie, Kentaro; Jiang, Jie A note on construction of nonnegative initial data inducing unbounded solutions to some two-dimensional Keller-Segel systems. (English) Zbl 1496.35076 Math. Eng. (Springfield) 4, No. 6, Paper No. 45, 12 p. (2022). MSC: 35B40 35B44 35K51 35K59 92C17 PDF BibTeX XML Cite \textit{K. Fujie} and \textit{J. Jiang}, Math. Eng. (Springfield) 4, No. 6, Paper No. 45, 12 p. (2022; Zbl 1496.35076) Full Text: DOI OpenURL
Bonheure, Denis; Casteras, Jean-Baptiste; Román, Carlos Unbounded mass radial solutions for the Keller-Segel equation in the disk. (English) Zbl 1472.35060 Calc. Var. Partial Differ. Equ. 60, No. 5, Paper No. 198, 30 p. (2021). MSC: 35B44 35B40 35B45 35J20 35J61 92C17 PDF BibTeX XML Cite \textit{D. Bonheure} et al., Calc. Var. Partial Differ. Equ. 60, No. 5, Paper No. 198, 30 p. (2021; Zbl 1472.35060) Full Text: DOI arXiv OpenURL
Ndjatchi, Mbe Koua Christophe; Vyridis, Panayotis; Martínez, Juan; Rosales, J. Juan On the non-negative radial solutions of the two dimensional Bratu equation. (English) Zbl 1488.35210 Kragujevac J. Math. 45, No. 2, 275-288 (2021). MSC: 35J25 35J60 PDF BibTeX XML Cite \textit{M. K. C. Ndjatchi} et al., Kragujevac J. Math. 45, No. 2, 275--288 (2021; Zbl 1488.35210) Full Text: Link OpenURL
Fujie, Kentarou; Jiang, Jie Comparison methods for a Keller-Segel-type model of pattern formations with density-suppressed motilities. (English) Zbl 1467.35044 Calc. Var. Partial Differ. Equ. 60, No. 3, Paper No. 92, 37 p. (2021). MSC: 35B36 35B40 35K51 35K59 35K65 92C17 PDF BibTeX XML Cite \textit{K. Fujie} and \textit{J. Jiang}, Calc. Var. Partial Differ. Equ. 60, No. 3, Paper No. 92, 37 p. (2021; Zbl 1467.35044) Full Text: DOI arXiv 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
Fujie, Kentarou; Jiang, Jie Global existence for a kinetic model of pattern formation with density-suppressed motilities. (English) Zbl 1440.35330 J. Differ. Equations 269, No. 6, 5338-5378 (2020). MSC: 35Q92 35B36 35K59 35B44 92C17 PDF BibTeX XML Cite \textit{K. Fujie} and \textit{J. Jiang}, J. Differ. Equations 269, No. 6, 5338--5378 (2020; Zbl 1440.35330) Full Text: DOI arXiv OpenURL
Bonheure, Denis; Casteras, Jean-Baptiste; Foldes, Juraj Singular radial solutions for the Keller-Segel equation in high dimension. (English. French summary) Zbl 1442.35156 J. Math. Pures Appl. (9) 134, 204-254 (2020). Reviewer: Alain Brillard (Riedisheim) MSC: 35J91 35J25 PDF BibTeX XML Cite \textit{D. Bonheure} et al., J. Math. Pures Appl. (9) 134, 204--254 (2020; Zbl 1442.35156) Full Text: DOI arXiv OpenURL
Honda, Hirotada On a model of target detection in molecular communication networks. (English) Zbl 1431.35078 Netw. Heterog. Media 14, No. 4, 633-657 (2019). MSC: 35K61 35Q92 92C17 PDF BibTeX XML Cite \textit{H. Honda}, Netw. Heterog. Media 14, No. 4, 633--657 (2019; Zbl 1431.35078) Full Text: DOI OpenURL
Braukhoff, Marcel; Lankeit, Johannes Stationary solutions to a chemotaxis-consumption model with realistic boundary conditions for the oxygen. (English) Zbl 1425.35196 Math. Models Methods Appl. Sci. 29, No. 11, 2033-2062 (2019). MSC: 35Q92 92C17 35J57 35A02 35B40 PDF BibTeX XML Cite \textit{M. Braukhoff} and \textit{J. Lankeit}, Math. Models Methods Appl. Sci. 29, No. 11, 2033--2062 (2019; Zbl 1425.35196) Full Text: DOI arXiv OpenURL
Wang, Jun; Wang, Zhian; Yang, Wen Uniqueness and convergence on equilibria of the Keller-Segel system with subcritical mass. (English) Zbl 1418.35189 Commun. Partial Differ. Equations 44, No. 7, 545-572 (2019). MSC: 35J91 35J25 PDF BibTeX XML Cite \textit{J. Wang} et al., Commun. Partial Differ. Equations 44, No. 7, 545--572 (2019; Zbl 1418.35189) Full Text: DOI arXiv OpenURL
Deng, Shengbing Construction solutions for Neumann problem with Hénon term in \( \mathbb{R}^2 \). (English) Zbl 1416.35118 Discrete Contin. Dyn. Syst. 39, No. 4, 2233-2253 (2019). MSC: 35J91 35J25 PDF BibTeX XML Cite \textit{S. Deng}, Discrete Contin. Dyn. Syst. 39, No. 4, 2233--2253 (2019; Zbl 1416.35118) Full Text: DOI OpenURL
Lin, Ke; Mu, Chunlai; Zhou, Deqin Stabilization in a higher-dimensional attraction-repulsion chemotaxis system if repulsion dominates over attraction. (English) Zbl 1391.35200 Math. Models Methods Appl. Sci. 28, No. 6, 1105-1134 (2018). MSC: 35K55 92C17 35B35 PDF BibTeX XML Cite \textit{K. Lin} et al., Math. Models Methods Appl. Sci. 28, No. 6, 1105--1134 (2018; Zbl 1391.35200) Full Text: DOI OpenURL
Bonheure, Denis; Casteras, Jean-Baptiste; Noris, Benedetta Multiple positive solutions of the stationary Keller-Segel system. (English) Zbl 1375.35097 Calc. Var. Partial Differ. Equ. 56, No. 3, Paper No. 74, 35 p. (2017). MSC: 35J05 35J61 35J25 35B32 PDF BibTeX XML Cite \textit{D. Bonheure} et al., Calc. Var. Partial Differ. Equ. 56, No. 3, Paper No. 74, 35 p. (2017; Zbl 1375.35097) Full Text: DOI arXiv OpenURL
Bonheure, Denis; Casteras, Jean-Baptiste; Noris, Benedetta Layered solutions with unbounded mass for the Keller-Segel equation. (English) Zbl 1375.35096 J. Fixed Point Theory Appl. 19, No. 1, 529-558 (2017). Reviewer: Alain Brillard (Riedisheim) MSC: 35J05 35B40 35B07 PDF BibTeX XML Cite \textit{D. Bonheure} et al., J. Fixed Point Theory Appl. 19, No. 1, 529--558 (2017; Zbl 1375.35096) Full Text: DOI OpenURL
Agudelo, Oscar; Pistoia, Angela Boundary concentration phenomena for the higher-dimensional Keller-Segel system. (English) Zbl 1366.35196 Calc. Var. Partial Differ. Equ. 55, No. 6, Paper No. 132, 31 p. (2016). Reviewer: Eugene Postnikov (Kursk) MSC: 35Q92 92C17 35J60 35B33 35J20 PDF BibTeX XML Cite \textit{O. Agudelo} and \textit{A. Pistoia}, Calc. Var. Partial Differ. Equ. 55, No. 6, Paper No. 132, 31 p. (2016; Zbl 1366.35196) Full Text: DOI arXiv OpenURL
del Pino, Manuel; Pistoia, Angela; Vaira, Giusi Large mass boundary condensation patterns in the stationary Keller-Segel system. (English) Zbl 1345.35039 J. Differ. Equations 261, No. 6, 3414-3462 (2016). Reviewer: Marius Ghergu (Dublin) MSC: 35J60 35B33 35J20 PDF BibTeX XML Cite \textit{M. del Pino} et al., J. Differ. Equations 261, No. 6, 3414--3462 (2016; Zbl 1345.35039) Full Text: DOI arXiv OpenURL
Gladiali, Francesca; Grossi, Massimo; Ohtsuka, Hiroshi On the number of peaks of the eigenfunctions of the linearized Gel’fand problem. (English) Zbl 1348.35061 Ann. Mat. Pura Appl. (4) 195, No. 1, 79-93 (2016). Reviewer: Bodo Dittmar (Halle) MSC: 35J15 35J60 PDF BibTeX XML Cite \textit{F. Gladiali} et al., Ann. Mat. Pura Appl. (4) 195, No. 1, 79--93 (2016; Zbl 1348.35061) Full Text: DOI arXiv OpenURL
Hichar, S.; Guerfi, A.; Douis, S.; Meftah, M. T. Application of nonlinear Bratu’s equation in two and three dimensions to electrostatics. (English) Zbl 1332.78007 Rep. Math. Phys. 76, No. 3, 283-290 (2015). MSC: 78A30 35Q60 PDF BibTeX XML Cite \textit{S. Hichar} et al., Rep. Math. Phys. 76, No. 3, 283--290 (2015; Zbl 1332.78007) Full Text: DOI OpenURL
Suzuki, Takashi Almost collapse mass quantization in 2D Smoluchowski-Poisson equation. (English) Zbl 1334.35108 Math. Methods Appl. Sci. 38, No. 16, 3587-3600 (2015). MSC: 35K55 85A15 92C17 35B44 PDF BibTeX XML Cite \textit{T. Suzuki}, Math. Methods Appl. Sci. 38, No. 16, 3587--3600 (2015; Zbl 1334.35108) Full Text: DOI arXiv OpenURL
Zhang, Qingshan; Li, Yuxiang Stabilization and convergence rate in a chemotaxis system with consumption of chemoattractant. (English) Zbl 1322.35060 J. Math. Phys. 56, No. 8, 081506, 10 p. (2015). MSC: 35K51 35K57 35K40 92C17 35B40 PDF BibTeX XML Cite \textit{Q. Zhang} and \textit{Y. Li}, J. Math. Phys. 56, No. 8, 081506, 10 p. (2015; Zbl 1322.35060) Full Text: DOI OpenURL
Tsujikawa, Tohru; Kuto, Kousuke; Miyamoto, Yasuhito; Izuhara, Hirofumi Stationary solutions for some shadow system of the Keller-Segel model with logistic growth. (English) Zbl 1320.35061 Discrete Contin. Dyn. Syst., Ser. S 8, No. 5, 1023-1034 (2015). MSC: 35B36 35B32 37G40 35K57 92C17 35B25 PDF BibTeX XML Cite \textit{T. Tsujikawa} et al., Discrete Contin. Dyn. Syst., Ser. S 8, No. 5, 1023--1034 (2015; Zbl 1320.35061) Full Text: DOI OpenURL
Suzuki, T. Exclusion of boundary blowup for 2D chemotaxis system provided with Dirichlet boundary condition for the Poisson part. (English) Zbl 1285.35121 J. Math. Pures Appl. (9) 100, No. 3, 347-367 (2013). MSC: 35Q92 92C17 PDF BibTeX XML Cite \textit{T. Suzuki}, J. Math. Pures Appl. (9) 100, No. 3, 347--367 (2013; Zbl 1285.35121) Full Text: DOI OpenURL
Wang, Xuefeng; Xu, Qian Spiky and transition layer steady states of chemotaxis systems via global bifurcation and Helly’s compactness theorem. (English) Zbl 1301.92006 J. Math. Biol. 66, No. 6, 1241-1266 (2013). MSC: 92C17 35B32 35J67 35B41 26A48 PDF BibTeX XML Cite \textit{X. Wang} and \textit{Q. Xu}, J. Math. Biol. 66, No. 6, 1241--1266 (2013; Zbl 1301.92006) Full Text: DOI OpenURL
Deng, Shengbing Mixed interior and boundary bubbling solutions for Neumann problem in \(\mathbb R^2\). (English) Zbl 1252.35031 J. Differ. Equations 253, No. 2, 727-763 (2012). Reviewer: Jiaqi Mo (Wuhu) MSC: 35B25 35J25 PDF BibTeX XML Cite \textit{S. Deng}, J. Differ. Equations 253, No. 2, 727--763 (2012; Zbl 1252.35031) Full Text: DOI 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
Lucia, Marcello Isoperimetric profile and uniqueness for Neumann problems. (English) Zbl 1159.58013 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26, No. 1, 81-100 (2009). Reviewer: Dian K. Palagachev (Bari) MSC: 58J05 53C21 35J60 PDF BibTeX XML Cite \textit{M. Lucia}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26, No. 1, 81--100 (2009; Zbl 1159.58013) Full Text: DOI EuDML OpenURL
Wei, Juncheng; Ye, Dong; Zhou, Feng Analysis of boundary bubbling solutions for an anisotropic Emden-Fowler equation. (English) Zbl 1155.35037 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 25, No. 3, 425-447 (2008). Reviewer: Maria Alessandra Ragusa (Catania) MSC: 35J60 35J65 35B40 35C05 PDF BibTeX XML Cite \textit{J. Wei} et al., Ann. Inst. Henri Poincaré, Anal. Non Linéaire 25, No. 3, 425--447 (2008; Zbl 1155.35037) Full Text: DOI EuDML OpenURL
Feireisl, Eduard; Laurençot, Philippe; Petzeltová, Hana On convergence to equilibria for the Keller-Segel chemotaxis model. (English) Zbl 1139.35018 J. Differ. Equations 236, No. 2, 551-569 (2007). MSC: 35B40 35K50 35K55 92C17 PDF BibTeX XML Cite \textit{E. Feireisl} et al., J. Differ. Equations 236, No. 2, 551--569 (2007; Zbl 1139.35018) Full Text: DOI OpenURL
Lucia, Marcello A deformation lemma for a Moser-Trudinger type functional. (English) Zbl 1139.35336 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 63, No. 2, 282-299 (2005). MSC: 35J20 35B38 35J60 47J30 58E05 PDF BibTeX XML Cite \textit{M. Lucia}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 63, No. 2, 282--299 (2005; Zbl 1139.35336) Full Text: DOI OpenURL
Nagai, Toshitaka; Nakaki, Tatsuyuki Stability of constant steady states and existence of unbounded solutions in time to a reaction–diffusion equation modelling chemotaxis. (English) Zbl 1083.35018 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 58, No. 5-6, 657-681 (2004). MSC: 35B35 35K50 35K57 92C17 35B32 PDF BibTeX XML Cite \textit{T. Nagai} and \textit{T. Nakaki}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 58, No. 5--6, 657--681 (2004; Zbl 1083.35018) Full Text: DOI OpenURL
Senba, Takasi; Suzuki, Takashi Weak solutions to a parabolic-elliptic system of chemotaxis. (English) Zbl 1005.35026 J. Funct. Anal. 191, No. 1, 17-51 (2002). Reviewer: Sebastian Aniţa (Iaşi) MSC: 35B60 92C17 PDF BibTeX XML Cite \textit{T. Senba} and \textit{T. Suzuki}, J. Funct. Anal. 191, No. 1, 17--51 (2002; Zbl 1005.35026) Full Text: DOI OpenURL