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Breakdown of $C^1$ solution to the Cauchy problem for quasilinear hyperbolic systems with characteristics with constant multiplicity
1. | Institute of Mathematics, Fudan University, Shanghai 200433, China |
[1] |
Xiuting Li, Lei Zhang. The Cauchy problem and blow-up phenomena for a new integrable two-component peakon system with cubic nonlinearities. Discrete and Continuous Dynamical Systems, 2017, 37 (6) : 3301-3325. doi: 10.3934/dcds.2017140 |
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Lingwei Ma, Zhong Bo Fang. A new second critical exponent and life span for a quasilinear degenerate parabolic equation with weighted nonlocal sources. Communications on Pure and Applied Analysis, 2017, 16 (5) : 1697-1706. doi: 10.3934/cpaa.2017081 |
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Cunming Liu, Jianli Liu. Stability of traveling wave solutions to Cauchy problem of diagnolizable quasilinear hyperbolic systems. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 4735-4749. doi: 10.3934/dcds.2014.34.4735 |
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Mohammad Kafini. On the blow-up of the Cauchy problem of higher-order nonlinear viscoelastic wave equation. Discrete and Continuous Dynamical Systems - S, 2022, 15 (5) : 1221-1232. doi: 10.3934/dcdss.2021093 |
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C. Brändle, F. Quirós, Julio D. Rossi. Non-simultaneous blow-up for a quasilinear parabolic system with reaction at the boundary. Communications on Pure and Applied Analysis, 2005, 4 (3) : 523-536. doi: 10.3934/cpaa.2005.4.523 |
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Johannes Lankeit. Infinite time blow-up of many solutions to a general quasilinear parabolic-elliptic Keller-Segel system. Discrete and Continuous Dynamical Systems - S, 2020, 13 (2) : 233-255. doi: 10.3934/dcdss.2020013 |
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Juntang Ding, Chenyu Dong. Blow-up results of the positive solution for a weakly coupled quasilinear parabolic system. Discrete and Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021222 |
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Yuya Tanaka, Tomomi Yokota. Finite-time blow-up in a quasilinear degenerate parabolic–elliptic chemotaxis system with logistic source and nonlinear production. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022075 |
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Meng-Rong Li. Estimates for the life-span of the solutions for some semilinear wave equations. Communications on Pure and Applied Analysis, 2008, 7 (2) : 417-432. doi: 10.3934/cpaa.2008.7.417 |
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Miaoqing Tian, Sining Zheng. Global boundedness versus finite-time blow-up of solutions to a quasilinear fully parabolic Keller-Segel system of two species. Communications on Pure and Applied Analysis, 2016, 15 (1) : 243-260. doi: 10.3934/cpaa.2016.15.243 |
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Todor Gramchev, Nicola Orrú. Cauchy problem for a class of nondiagonalizable hyperbolic systems. Conference Publications, 2011, 2011 (Special) : 533-542. doi: 10.3934/proc.2011.2011.533 |
[12] |
Yoshikazu Giga. Interior derivative blow-up for quasilinear parabolic equations. Discrete and Continuous Dynamical Systems, 1995, 1 (3) : 449-461. doi: 10.3934/dcds.1995.1.449 |
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Jong-Shenq Guo. Blow-up behavior for a quasilinear parabolic equation with nonlinear boundary condition. Discrete and Continuous Dynamical Systems, 2007, 18 (1) : 71-84. doi: 10.3934/dcds.2007.18.71 |
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Marina Chugunova, Chiu-Yen Kao, Sarun Seepun. On the Benilov-Vynnycky blow-up problem. Discrete and Continuous Dynamical Systems - B, 2015, 20 (5) : 1443-1460. doi: 10.3934/dcdsb.2015.20.1443 |
[15] |
Victor A. Galaktionov, Juan-Luis Vázquez. The problem Of blow-up in nonlinear parabolic equations. Discrete and Continuous Dynamical Systems, 2002, 8 (2) : 399-433. doi: 10.3934/dcds.2002.8.399 |
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Tong Li, Kun Zhao. On a quasilinear hyperbolic system in blood flow modeling. Discrete and Continuous Dynamical Systems - B, 2011, 16 (1) : 333-344. doi: 10.3934/dcdsb.2011.16.333 |
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Felipe Linares, M. Panthee. On the Cauchy problem for a coupled system of KdV equations. Communications on Pure and Applied Analysis, 2004, 3 (3) : 417-431. doi: 10.3934/cpaa.2004.3.417 |
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Juliana Fernandes, Liliane Maia. Blow-up and bounded solutions for a semilinear parabolic problem in a saturable medium. Discrete and Continuous Dynamical Systems, 2021, 41 (3) : 1297-1318. doi: 10.3934/dcds.2020318 |
[19] |
Pierpaolo Esposito, Maristella Petralla. Symmetries and blow-up phenomena for a Dirichlet problem with a large parameter. Communications on Pure and Applied Analysis, 2012, 11 (5) : 1935-1957. doi: 10.3934/cpaa.2012.11.1935 |
[20] |
Yihong Du, Zongming Guo, Feng Zhou. Boundary blow-up solutions with interior layers and spikes in a bistable problem. Discrete and Continuous Dynamical Systems, 2007, 19 (2) : 271-298. doi: 10.3934/dcds.2007.19.271 |
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