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Global solutions and selfsimilar solutions of the coupled system of semilinear wave equations in three space dimensions
1.  Department of Applied Mathematics, Faculty of Engineering, Shizuoka University, Hamamatsu 4328561, Japan 
2.  Mathematical Institute, Tohoku University, Sendai 9808578, Japan 
[1] 
Weronika Biedrzycka, Marta TyranKamińska. Selfsimilar solutions of fragmentation equations revisited. Discrete & Continuous Dynamical Systems  B, 2018, 23 (1) : 1327. doi: 10.3934/dcdsb.2018002 
[2] 
Shota Sato, Eiji Yanagida. Singular backward selfsimilar solutions of a semilinear parabolic equation. Discrete & Continuous Dynamical Systems  S, 2011, 4 (4) : 897906. doi: 10.3934/dcdss.2011.4.897 
[3] 
Marek Fila, Michael Winkler, Eiji Yanagida. Convergence to selfsimilar solutions for a semilinear parabolic equation. Discrete & Continuous Dynamical Systems  A, 2008, 21 (3) : 703716. doi: 10.3934/dcds.2008.21.703 
[4] 
Qiaolin He. Numerical simulation and selfsimilar analysis of singular solutions of Prandtl equations. Discrete & Continuous Dynamical Systems  B, 2010, 13 (1) : 101116. doi: 10.3934/dcdsb.2010.13.101 
[5] 
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 
[6] 
Hyungjin Huh. Selfsimilar solutions to nonlinear Dirac equations and an application to nonuniqueness. Evolution Equations & Control Theory, 2018, 7 (1) : 5360. doi: 10.3934/eect.2018003 
[7] 
Marco Cannone, Grzegorz Karch. On selfsimilar solutions to the homogeneous Boltzmann equation. Kinetic & Related Models, 2013, 6 (4) : 801808. doi: 10.3934/krm.2013.6.801 
[8] 
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 
[9] 
Zoran Grujić. Regularity of forwardintime selfsimilar solutions to the 3D NavierStokes equations. Discrete & Continuous Dynamical Systems  A, 2006, 14 (4) : 837843. doi: 10.3934/dcds.2006.14.837 
[10] 
Bendong Lou. Selfsimilar solutions in a sector for a quasilinear parabolic equation. Networks & Heterogeneous Media, 2012, 7 (4) : 857879. doi: 10.3934/nhm.2012.7.857 
[11] 
Kin Ming Hui. Existence of selfsimilar solutions of the inverse mean curvature flow. Discrete & Continuous Dynamical Systems  A, 2019, 39 (2) : 863880. doi: 10.3934/dcds.2019036 
[12] 
Shota Sato, Eiji Yanagida. Forward selfsimilar solution with a moving singularity for a semilinear parabolic equation. Discrete & Continuous Dynamical Systems  A, 2010, 26 (1) : 313331. doi: 10.3934/dcds.2010.26.313 
[13] 
K. T. Joseph, Philippe G. LeFloch. Boundary layers in weak solutions of hyperbolic conservation laws II. selfsimilar vanishing diffusion limits. Communications on Pure & Applied Analysis, 2002, 1 (1) : 5176. doi: 10.3934/cpaa.2002.1.51 
[14] 
Meiyue Jiang, Juncheng Wei. $2\pi$Periodic selfsimilar solutions for the anisotropic affine curve shortening problem II. Discrete & Continuous Dynamical Systems  A, 2016, 36 (2) : 785803. doi: 10.3934/dcds.2016.36.785 
[15] 
Adrien Blanchet, Philippe Laurençot. Finite mass selfsimilar blowingup solutions of a chemotaxis system with nonlinear diffusion. Communications on Pure & Applied Analysis, 2012, 11 (1) : 4760. doi: 10.3934/cpaa.2012.11.47 
[16] 
Kosuke Ono. Global existence and asymptotic behavior of small solutions for semilinear dissipative wave equations. Discrete & Continuous Dynamical Systems  A, 2003, 9 (3) : 651662. doi: 10.3934/dcds.2003.9.651 
[17] 
Dongbing Zha, Yi Zhou. The lifespan for quasilinear wave equations with multiple propagation speeds in four space dimensions. Communications on Pure & Applied Analysis, 2014, 13 (3) : 11671186. doi: 10.3934/cpaa.2014.13.1167 
[18] 
Thomas Y. Hou, Ruo Li. Nonexistence of locally selfsimilar blowup for the 3D incompressible NavierStokes equations. Discrete & Continuous Dynamical Systems  A, 2007, 18 (4) : 637642. doi: 10.3934/dcds.2007.18.637 
[19] 
Dongho Chae, Kyungkeun Kang, Jihoon Lee. Notes on the asymptotically selfsimilar singularities in the Euler and the NavierStokes equations. Discrete & Continuous Dynamical Systems  A, 2009, 25 (4) : 11811193. doi: 10.3934/dcds.2009.25.1181 
[20] 
Rostislav Grigorchuk, Volodymyr Nekrashevych. Selfsimilar groups, operator algebras and Schur complement. Journal of Modern Dynamics, 2007, 1 (3) : 323370. doi: 10.3934/jmd.2007.1.323 
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