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Regularity of extremal solutions in fourth order nonlinear eigenvalue problems on general domains
Limiting profiles of semilinear elliptic equations with large advection in population dynamics
1.  School of Mathematics, University of Minnesota, Minneapolis, MN 55455, United States 
2.  School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455 
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Haitao Yang. On the existence and asymptotic behavior of large solutions for a semilinear elliptic problem in $R^n$. Communications on Pure & Applied Analysis, 2005, 4 (1) : 187198. doi: 10.3934/cpaa.2005.4.197 
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David Aleja, Julián LópezGómez. Some paradoxical effects of the advection on a class of diffusive equations in Ecology. Discrete & Continuous Dynamical Systems  B, 2014, 19 (10) : 30313056. doi: 10.3934/dcdsb.2014.19.3031 
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Zhijun Zhang. Large solutions of semilinear elliptic equations with a gradient term: existence and boundary behavior. Communications on Pure & Applied Analysis, 2013, 12 (3) : 13811392. doi: 10.3934/cpaa.2013.12.1381 
[4] 
Akisato Kubo. Asymptotic behavior of solutions of the mixed problem for semilinear hyperbolic equations. Communications on Pure & Applied Analysis, 2004, 3 (1) : 5974. doi: 10.3934/cpaa.2004.3.59 
[5] 
Hideo Kubo. Asymptotic behavior of solutions to semilinear wave equations with dissipative structure. Conference Publications, 2007, 2007 (Special) : 602613. doi: 10.3934/proc.2007.2007.602 
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Kazuhiro Ishige, Tatsuki Kawakami. Asymptotic behavior of solutions for some semilinear heat equations in $R^N$. Communications on Pure & Applied Analysis, 2009, 8 (4) : 13511371. doi: 10.3934/cpaa.2009.8.1351 
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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 
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Xinhua Zhao, Zilai Li. Asymptotic behavior of spherically or cylindrically symmetric solutions to the compressible NavierStokes equations with large initial data. Communications on Pure & Applied Analysis, 2020, 19 (3) : 14211448. doi: 10.3934/cpaa.2020052 
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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 
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Sandra Lucente. Large data solutions for semilinear higher order equations. Discrete & Continuous Dynamical Systems  S, 2020 doi: 10.3934/dcdss.2020247 
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Kin Ming Hui, Soojung Kim. Asymptotic large time behavior of singular solutions of the fast diffusion equation. Discrete & Continuous Dynamical Systems  A, 2017, 37 (11) : 59435977. doi: 10.3934/dcds.2017258 
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Qiong Chen, Chunlai Mu, Zhaoyin Xiang. Blowup and asymptotic behavior of solutions to a semilinear integrodifferential system. Communications on Pure & Applied Analysis, 2006, 5 (3) : 435446. doi: 10.3934/cpaa.2006.5.435 
[14] 
Jingyu Li. Asymptotic behavior of solutions to elliptic equations in a coated body. Communications on Pure & Applied Analysis, 2009, 8 (4) : 12511267. doi: 10.3934/cpaa.2009.8.1251 
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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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Yutian Lei, Chao Ma. Asymptotic behavior for solutions of some integral equations. Communications on Pure & Applied Analysis, 2011, 10 (1) : 193207. doi: 10.3934/cpaa.2011.10.193 
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Yadong Shang, Jianjun Paul Tian, Bixiang Wang. Asymptotic behavior of the stochastic KellerSegel equations. Discrete & Continuous Dynamical Systems  B, 2019, 24 (3) : 13671391. doi: 10.3934/dcdsb.2019020 
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Alan V. Lair, Ahmed Mohammed. Entire large solutions of semilinear elliptic equations of mixed type. Communications on Pure & Applied Analysis, 2009, 8 (5) : 16071618. doi: 10.3934/cpaa.2009.8.1607 
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Zhijun Zhang, Ling Mi. Blowup rates of large solutions for semilinear elliptic equations. Communications on Pure & Applied Analysis, 2011, 10 (6) : 17331745. doi: 10.3934/cpaa.2011.10.1733 
[20] 
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 
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