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Mechanism of the formation of singularities for diagonal systems with linearly degenerate characteristic fields
1.  Department of Mathematics, College of Sciences, Hohai University, Nanjing 210098, Jiangsu, China 
[1] 
Tatsien Li, Libin Wang. Global classical solutions to a kind of mixed initialboundary value problem for quasilinear hyperbolic systems. Discrete and Continuous Dynamical Systems, 2005, 12 (1) : 5978. doi: 10.3934/dcds.2005.12.59 
[2] 
Tatsien Li, Bopeng Rao, Zhiqiang Wang. A note on the oneside exact boundary controllability for quasilinear hyperbolic systems. Communications on Pure and Applied Analysis, 2009, 8 (1) : 405418. doi: 10.3934/cpaa.2009.8.405 
[3] 
Xiaoyun Cai, Liangwen Liao, Yongzhong Sun. Global strong solution to the initialboundary value problem of a 2D KazhikhovSmagulov type model. Discrete and Continuous Dynamical Systems  S, 2014, 7 (5) : 917923. doi: 10.3934/dcdss.2014.7.917 
[4] 
Peng Jiang. Unique global solution of an initialboundary value problem to a diffusion approximation model in radiation hydrodynamics. Discrete and Continuous Dynamical Systems, 2015, 35 (7) : 30153037. doi: 10.3934/dcds.2015.35.3015 
[5] 
Libin Wang. Breakdown of $C^1$ solution to the Cauchy problem for quasilinear hyperbolic systems with characteristics with constant multiplicity. Communications on Pure and Applied Analysis, 2003, 2 (1) : 7789. doi: 10.3934/cpaa.2003.2.77 
[6] 
ZhiQiang Shao. Global existence of classical solutions of Goursat problem for quasilinear hyperbolic systems of diagonal form with large BV data. Communications on Pure and Applied Analysis, 2013, 12 (6) : 27392752. doi: 10.3934/cpaa.2013.12.2739 
[7] 
Martn P. Árciga Alejandre, Elena I. Kaikina. Mixed initialboundary value problem for OttSudanOstrovskiy equation. Discrete and Continuous Dynamical Systems, 2012, 32 (2) : 381409. doi: 10.3934/dcds.2012.32.381 
[8] 
Michal Beneš. Mixed initialboundary value problem for the threedimensional NavierStokes equations in polyhedral domains. Conference Publications, 2011, 2011 (Special) : 135144. doi: 10.3934/proc.2011.2011.135 
[9] 
Shaoyong Lai, Yong Hong Wu, Xu Yang. The global solution of an initial boundary value problem for the damped Boussinesq equation. Communications on Pure and Applied Analysis, 2004, 3 (2) : 319328. doi: 10.3934/cpaa.2004.3.319 
[10] 
Gilles Carbou, Bernard Hanouzet. Relaxation approximation of the Kerr model for the impedance initialboundary value problem. Conference Publications, 2007, 2007 (Special) : 212220. doi: 10.3934/proc.2007.2007.212 
[11] 
Xianpeng Hu, Dehua Wang. The initialboundary value problem for the compressible viscoelastic flows. Discrete and Continuous Dynamical Systems, 2015, 35 (3) : 917934. doi: 10.3934/dcds.2015.35.917 
[12] 
Yi Zhou, Jianli Liu. The initialboundary value problem on a strip for the equation of timelike extremal surfaces. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 381397. doi: 10.3934/dcds.2009.23.381 
[13] 
Türker Özsarı, Nermin Yolcu. The initialboundary value problem for the biharmonic Schrödinger equation on the halfline. Communications on Pure and Applied Analysis, 2019, 18 (6) : 32853316. doi: 10.3934/cpaa.2019148 
[14] 
Haifeng Hu, Kaijun Zhang. Analysis on the initialboundary value problem of a full bipolar hydrodynamic model for semiconductors. Discrete and Continuous Dynamical Systems  B, 2014, 19 (6) : 16011626. doi: 10.3934/dcdsb.2014.19.1601 
[15] 
Boling Guo, Jun Wu. Wellposedness of the initialboundary value problem for the fourthorder nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems  B, 2022, 27 (7) : 37493778. doi: 10.3934/dcdsb.2021205 
[16] 
Peicheng Zhu, Lei Yu, Yang Xiang. Weak solutions to an initialboundary value problem for a continuum equation of motion of grain boundaries. Discrete and Continuous Dynamical Systems  B, 2022 doi: 10.3934/dcdsb.2022139 
[17] 
Xu Liu, Jun Zhou. Initialboundary value problem for a fourthorder plate equation with HardyHénon potential and polynomial nonlinearity. Electronic Research Archive, 2020, 28 (2) : 599625. doi: 10.3934/era.2020032 
[18] 
Linglong Du, Caixuan Ren. Pointwise wave behavior of the initialboundary value problem for the nonlinear damped wave equation in $\mathbb{R}_{+}^{n} $. Discrete and Continuous Dynamical Systems  B, 2019, 24 (7) : 32653280. doi: 10.3934/dcdsb.2018319 
[19] 
ZhiQiang Shao. Lifespan of classical discontinuous solutions to the generalized nonlinear initialboundary Riemann problem for hyperbolic conservation laws with small BV data: shocks and contact discontinuities. Communications on Pure and Applied Analysis, 2015, 14 (3) : 759792. doi: 10.3934/cpaa.2015.14.759 
[20] 
Yang Cao, Qiuting Zhao. Initial boundary value problem of a class of mixed pseudoparabolic Kirchhoff equations. Electronic Research Archive, 2021, 29 (6) : 38333851. doi: 10.3934/era.2021064 
2021 Impact Factor: 1.273
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