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Finite mass selfsimilar blowingup solutions of a chemotaxis system with nonlinear diffusion
1.  GREMAQ, CNRS UMR 5604, INRA UMR 1291, Université de Toulouse, 21 Allée de Brienne, F31000 Toulouse, France 
2.  Institut de Mathématiques de Toulouse, CNRS UMR 5219, Université de Toulouse, F–31062 Toulouse cedex 9 
References:
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References:
[1] 
Tian Xiang. On effects of sampling radius for the nonlocal PatlakKellerSegel chemotaxis model. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 49114946. doi: 10.3934/dcds.2014.34.4911 
[2] 
Jacob Bedrossian, Nancy Rodríguez. Inhomogeneous PatlakKellerSegel models and aggregation equations with nonlinear diffusion in $\mathbb{R}^d$. Discrete and Continuous Dynamical Systems  B, 2014, 19 (5) : 12791309. doi: 10.3934/dcdsb.2014.19.1279 
[3] 
Shota Sato, Eiji Yanagida. Singular backward selfsimilar solutions of a semilinear parabolic equation. Discrete and Continuous Dynamical Systems  S, 2011, 4 (4) : 897906. doi: 10.3934/dcdss.2011.4.897 
[4] 
Weronika Biedrzycka, Marta TyranKamińska. Selfsimilar solutions of fragmentation equations revisited. Discrete and Continuous Dynamical Systems  B, 2018, 23 (1) : 1327. doi: 10.3934/dcdsb.2018002 
[5] 
Marco Cannone, Grzegorz Karch. On selfsimilar solutions to the homogeneous Boltzmann equation. Kinetic and Related Models, 2013, 6 (4) : 801808. doi: 10.3934/krm.2013.6.801 
[6] 
K. T. Joseph, Philippe G. LeFloch. Boundary layers in weak solutions of hyperbolic conservation laws II. selfsimilar vanishing diffusion limits. Communications on Pure and Applied Analysis, 2002, 1 (1) : 5176. doi: 10.3934/cpaa.2002.1.51 
[7] 
Jochen Merker, Aleš Matas. Positivity of selfsimilar solutions of doubly nonlinear reactiondiffusion equations. Conference Publications, 2015, 2015 (special) : 817825. doi: 10.3934/proc.2015.0817 
[8] 
Kin Ming Hui. Existence of selfsimilar solutions of the inverse mean curvature flow. Discrete and Continuous Dynamical Systems, 2019, 39 (2) : 863880. doi: 10.3934/dcds.2019036 
[9] 
Qiaolin He. Numerical simulation and selfsimilar analysis of singular solutions of Prandtl equations. Discrete and Continuous Dynamical Systems  B, 2010, 13 (1) : 101116. doi: 10.3934/dcdsb.2010.13.101 
[10] 
Bendong Lou. Selfsimilar solutions in a sector for a quasilinear parabolic equation. Networks and Heterogeneous Media, 2012, 7 (4) : 857879. doi: 10.3934/nhm.2012.7.857 
[11] 
F. Berezovskaya, G. Karev. Bifurcations of selfsimilar solutions of the FokkerPlank equations. Conference Publications, 2005, 2005 (Special) : 9199. doi: 10.3934/proc.2005.2005.91 
[12] 
Alberto Bressan, Wen Shen. A posteriori error estimates for selfsimilar solutions to the Euler equations. Discrete and Continuous Dynamical Systems, 2021, 41 (1) : 113130. doi: 10.3934/dcds.2020168 
[13] 
Marek Fila, Michael Winkler, Eiji Yanagida. Convergence to selfsimilar solutions for a semilinear parabolic equation. Discrete and Continuous Dynamical Systems, 2008, 21 (3) : 703716. doi: 10.3934/dcds.2008.21.703 
[14] 
Hyungjin Huh. Selfsimilar solutions to nonlinear Dirac equations and an application to nonuniqueness. Evolution Equations and Control Theory, 2018, 7 (1) : 5360. doi: 10.3934/eect.2018003 
[15] 
Wenting Cong, JianGuo Liu. A degenerate $p$Laplacian KellerSegel model. Kinetic and Related Models, 2016, 9 (4) : 687714. doi: 10.3934/krm.2016012 
[16] 
Kenneth H. Karlsen, Süleyman Ulusoy. On a hyperbolic KellerSegel system with degenerate nonlinear fractional diffusion. Networks and Heterogeneous Media, 2016, 11 (1) : 181201. doi: 10.3934/nhm.2016.11.181 
[17] 
Razvan Gabriel Iagar, Ana Isabel Muñoz, Ariel Sánchez. Selfsimilar blowup patterns for a reactiondiffusion equation with weighted reaction in general dimension. Communications on Pure and Applied Analysis, 2022, 21 (3) : 891925. doi: 10.3934/cpaa.2022003 
[18] 
Yajing Zhang, Xinfu Chen, Jianghao Hao, Xin Lai, Cong Qin. Dynamics of spike in a KellerSegel's minimal chemotaxis model. Discrete and Continuous Dynamical Systems, 2017, 37 (2) : 11091127. doi: 10.3934/dcds.2017046 
[19] 
Hideo Kubo, Kotaro Tsugawa. Global solutions and selfsimilar solutions of the coupled system of semilinear wave equations in three space dimensions. Discrete and Continuous Dynamical Systems, 2003, 9 (2) : 471482. doi: 10.3934/dcds.2003.9.471 
[20] 
Meiyue Jiang, Juncheng Wei. $2\pi$Periodic selfsimilar solutions for the anisotropic affine curve shortening problem II. Discrete and Continuous Dynamical Systems, 2016, 36 (2) : 785803. doi: 10.3934/dcds.2016.36.785 
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