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Generalized fronts for onedimensional reactiondiffusion equations
Forward selfsimilar solution with a moving singularity for a semilinear parabolic equation
1.  Mathematical Institute, Tohoku University, Sendai 9808578, Japan 
2.  Mathematical Institute Tohoku University, 63Aoba, Aramaki, Aobaku, Sendaishi, 9808578 
[1] 
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 
[2] 
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 
[3] 
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 
[4] 
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 
[5] 
Zoran Grujić. Regularity of forwardintime selfsimilar solutions to the 3D NavierStokes equations. Discrete and Continuous Dynamical Systems, 2006, 14 (4) : 837843. doi: 10.3934/dcds.2006.14.837 
[6] 
Francis Hounkpe, Gregory Seregin. An approximation of forward selfsimilar solutions to the 3D NavierStokes system. Discrete and Continuous Dynamical Systems, 2021, 41 (10) : 48234846. doi: 10.3934/dcds.2021059 
[7] 
Shota Sato. Blowup at space infinity of a solution with a moving singularity for a semilinear parabolic equation. Communications on Pure and Applied Analysis, 2011, 10 (4) : 12251237. doi: 10.3934/cpaa.2011.10.1225 
[8] 
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 
[9] 
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 
[10] 
Juncheng Wei, Ke Wu. Local behavior of solutions to a fractional equation with isolated singularity and critical Serrin exponent. Discrete and Continuous Dynamical Systems, 2022, 42 (8) : 40314050. doi: 10.3934/dcds.2022044 
[11] 
Maurizio Grasselli, Vittorino Pata. On the damped semilinear wave equation with critical exponent. Conference Publications, 2003, 2003 (Special) : 351358. doi: 10.3934/proc.2003.2003.351 
[12] 
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 
[13] 
Li Ma. Blowup for semilinear parabolic equations with critical Sobolev exponent. Communications on Pure and Applied Analysis, 2013, 12 (2) : 11031110. doi: 10.3934/cpaa.2013.12.1103 
[14] 
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 
[15] 
Christoph Bandt, Helena PeÑa. Polynomial approximation of selfsimilar measures and the spectrum of the transfer operator. Discrete and Continuous Dynamical Systems, 2017, 37 (9) : 46114623. doi: 10.3934/dcds.2017198 
[16] 
Anna Chiara Lai, Paola Loreti. Selfsimilar control systems and applications to zygodactyl bird's foot. Networks and Heterogeneous Media, 2015, 10 (2) : 401419. doi: 10.3934/nhm.2015.10.401 
[17] 
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 
[18] 
D. G. Aronson. Selfsimilar focusing in porous media: An explicit calculation. Discrete and Continuous Dynamical Systems  B, 2012, 17 (6) : 16851691. doi: 10.3934/dcdsb.2012.17.1685 
[19] 
G. A. Braga, Frederico Furtado, Vincenzo Isaia. Renormalization group calculation of asymptotically selfsimilar dynamics. Conference Publications, 2005, 2005 (Special) : 131141. doi: 10.3934/proc.2005.2005.131 
[20] 
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 
2021 Impact Factor: 1.588
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