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Decay of solutions to nonlinear parabolic equations: renormalization and rigorous results
1.  Department of Mathematics, University of Pittsburg, Pittsburgh, PA 15260, United States 
2.  Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, United States 
[1] 
P. R. Zingano. Asymptotic behavior of the $L^1$ norm of solutions to nonlinear parabolic equations. Communications on Pure & Applied Analysis, 2004, 3 (1) : 151159. doi: 10.3934/cpaa.2004.3.151 
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ChiuYa Lan, ChiKun Lin. Asymptotic behavior of the compressible viscous potential fluid: Renormalization group approach. Discrete & Continuous Dynamical Systems  A, 2004, 11 (1) : 161188. doi: 10.3934/dcds.2004.11.161 
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G. A. Braga, Frederico Furtado, Jussara M. Moreira, Leonardo T. Rolla. Renormalization group analysis of nonlinear diffusion equations with time dependent coefficients: Analytical results. Discrete & Continuous Dynamical Systems  B, 2007, 7 (4) : 699715. doi: 10.3934/dcdsb.2007.7.699 
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Lie Zheng. Asymptotic behavior of solutions to the nonlinear breakage equations. Communications on Pure & Applied Analysis, 2005, 4 (2) : 463473. doi: 10.3934/cpaa.2005.4.463 
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Chunqing Lu. Asymptotic solutions of a nonlinear equation. Conference Publications, 2003, 2003 (Special) : 590595. doi: 10.3934/proc.2003.2003.590 
[6] 
Huijiang Zhao. Large time decay estimates of solutions of nonlinear parabolic equations. Discrete & Continuous Dynamical Systems  A, 2002, 8 (1) : 69114. doi: 10.3934/dcds.2002.8.69 
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Chunpeng Wang. Boundary behavior and asymptotic behavior of solutions to a class of parabolic equations with boundary degeneracy. Discrete & Continuous Dynamical Systems  A, 2016, 36 (2) : 10411060. doi: 10.3934/dcds.2016.36.1041 
[8] 
Limei Dai. Entire solutions with asymptotic behavior of fully nonlinear uniformly elliptic equations. Communications on Pure & Applied Analysis, 2011, 10 (6) : 17071714. doi: 10.3934/cpaa.2011.10.1707 
[9] 
Zdeněk Skalák. On the asymptotic decay of higherorder norms of the solutions to the NavierStokes equations in R^{3}. Discrete & Continuous Dynamical Systems  S, 2010, 3 (2) : 361370. doi: 10.3934/dcdss.2010.3.361 
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Peter V. Gordon, Cyrill B. Muratov. Selfsimilarity and longtime behavior of solutions of the diffusion equation with nonlinear absorption and a boundary source. Networks & Heterogeneous Media, 2012, 7 (4) : 767780. doi: 10.3934/nhm.2012.7.767 
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Thomas Blanc, Mihai Bostan, Franck Boyer. Asymptotic analysis of parabolic equations with stiff transport terms by a multiscale approach. Discrete & Continuous Dynamical Systems  A, 2017, 37 (9) : 46374676. doi: 10.3934/dcds.2017200 
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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 
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Minkyu Kwak, Kyong Yu. The asymptotic behavior of solutions of a semilinear parabolic equation. Discrete & Continuous Dynamical Systems  A, 1996, 2 (4) : 483496. doi: 10.3934/dcds.1996.2.483 
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Shota Sato, Eiji Yanagida. Asymptotic behavior of singular solutions for a semilinear parabolic equation. Discrete & Continuous Dynamical Systems  A, 2012, 32 (11) : 40274043. doi: 10.3934/dcds.2012.32.4027 
[15] 
Kun Wang, Yangping Lin, Yinnian He. Asymptotic analysis of the equations of motion for viscoelastic oldroyd fluid. Discrete & Continuous Dynamical Systems  A, 2012, 32 (2) : 657677. doi: 10.3934/dcds.2012.32.657 
[16] 
Hua Chen, Nian Liu. Asymptotic stability and blowup of solutions for semilinear edgedegenerate parabolic equations with singular potentials. Discrete & Continuous Dynamical Systems  A, 2016, 36 (2) : 661682. doi: 10.3934/dcds.2016.36.661 
[17] 
Junde Wu, Shangbin Cui. Asymptotic behavior of solutions for parabolic differential equations with invariance and applications to a free boundary problem modeling tumor growth. Discrete & Continuous Dynamical Systems  A, 2010, 26 (2) : 737765. doi: 10.3934/dcds.2010.26.737 
[18] 
PaoLiu Chow. Asymptotic solutions of a nonlinear stochastic beam equation. Discrete & Continuous Dynamical Systems  B, 2006, 6 (4) : 735749. doi: 10.3934/dcdsb.2006.6.735 
[19] 
Yongqin Liu. Asymptotic behavior of solutions to a nonlinear plate equation with memory. Communications on Pure & Applied Analysis, 2017, 16 (2) : 533556. doi: 10.3934/cpaa.2017027 
[20] 
Irena Lasiecka, W. Heyman. Asymptotic behavior of solutions in nonlinear dynamic elasticity. Discrete & Continuous Dynamical Systems  A, 1995, 1 (2) : 237252. doi: 10.3934/dcds.1995.1.237 
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