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Long time behavior of solutions to a Schrödinger-Poisson system in $R^3$
Global and blowup solutions for general Lotka-Volterra systems
1. | School of Science and Technology, Cape Breton University, Sydney, NS, Canada, B1P 6L2, Canada |
2. | College of Science, Harbin Engineering University, Harbin 150001, China, China |
References:
[1] |
S. Chen, Global existence and nonexistence for some degenerate and quasilinear parabolic systems, J. Differential Equations, 245 (2008), 1112-1136.
doi: 10.1016/j.jde.2007.11.008. |
[2] |
S. Chen, Boundedness and blowup solutions for quasilinear parabolic systems with lower order terms, Comm. Pure Appl. Anal., 8 (2009), 587-600.
doi: 10.3934/cpaa.2009.8.587. |
[3] |
S. Chen and K. MacDonald, Global and blowup solutions for general quasilinear parabolic systems, Nonlinear Anal. RWA, 14 (2013), 423-433.
doi: 10.1016/j.nonrwa.2012.07.006. |
[4] |
W. Deng, Global existence and finite time blow up for a degenerate reaction-diffusion system, Nonlinear Anal., 60 (2005), 977-991.
doi: 10.1016/j.na.2004.10.016. |
[5] |
Y. Han and W. Gao, A degenerate and strongly coupled quasilinear parabolic system with crosswise diffusion for a mutualistic model, Nonlinear Anal. RWA, 11 (2010), 3421-3430.
doi: 10.1016/j.nonrwa.2009.12.002. |
[6] |
V. A. Galaktionov and J. L. Vazquez, The problem of blow-up in nonlinear parabolic equations, Discrete Contin. Dyn. Syst., 8 (2002), 399-433.
doi: 10.3934/dcds.2002.8.399. |
[7] |
K. Kim and Z. Lin, A degenerate parabolic system with self-diffusion for a mutualistic model in ecology, Nonlinear Anal. RWA, 7 (2006), 597-609.
doi: 10.1016/j.nonrwa.2005.03.020. |
[8] |
O. A. Ladyzenskaja, V. A. Solonnikov and N. N. Uralceva, Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc., Providence, 1967. |
[9] |
C. Mu, X. Hu, Y. Li and Z. Cui, Blow-up and global existence for a coupled system of degenerte parabolic equations in a bounded domain, Acta Math. Sci., 27B (2007), 92-106.
doi: 10.1016/S0252-9602(07)60008-3. |
[10] |
C. V. Pao, A Lotka-Volterra cooperating reaction-diffusion system with degenerate density-dependent diffusion, Nonl. Anal., 95 (2014), 460-467.
doi: 10.1016/j.na.2013.09.015. |
[11] |
C. V. Pao, Dynamics of Lotka-Volterra competition reaction-diffusion systems with degenerate diffusion, J. Math. Anal. Appl., 421 (2015), 1721-1742.
doi: 10.1016/j.jmaa.2014.07.070. |
[12] |
C. V. Pao and W. H. Ruan, Quasilinear parabolic and elliptic systems with mixed quasimonotone functions, J. Differential Equations, 255 (2013), 1515-1553.
doi: 10.1016/j.jde.2013.05.015. |
[13] |
M. Wang, Some degenerate and quasilinear parabolic systems not in divergence form, J. Math. Anal. Appl., 274 (2002), 424-436.
doi: 10.1016/S0022-247X(02)00347-5. |
[14] |
M. Wang and C. Xie, A degenerate and strongly coupled quasilinear parabolic system not in divergence form, Z. Angew. Math. Phys., 55 (2004), 741-755.
doi: 10.1007/s00033-004-1133-4. |
[15] |
W. Yang, J. Wu and H. Nie, Some uniqueness and multiplicity results for a predator-prey dynamics with a nonlinear growth rate, Commun. Pure Appl. Anal., 14 (2015), 1183-1204.
doi: 10.3934/cpaa.2015.14.1183. |
show all references
References:
[1] |
S. Chen, Global existence and nonexistence for some degenerate and quasilinear parabolic systems, J. Differential Equations, 245 (2008), 1112-1136.
doi: 10.1016/j.jde.2007.11.008. |
[2] |
S. Chen, Boundedness and blowup solutions for quasilinear parabolic systems with lower order terms, Comm. Pure Appl. Anal., 8 (2009), 587-600.
doi: 10.3934/cpaa.2009.8.587. |
[3] |
S. Chen and K. MacDonald, Global and blowup solutions for general quasilinear parabolic systems, Nonlinear Anal. RWA, 14 (2013), 423-433.
doi: 10.1016/j.nonrwa.2012.07.006. |
[4] |
W. Deng, Global existence and finite time blow up for a degenerate reaction-diffusion system, Nonlinear Anal., 60 (2005), 977-991.
doi: 10.1016/j.na.2004.10.016. |
[5] |
Y. Han and W. Gao, A degenerate and strongly coupled quasilinear parabolic system with crosswise diffusion for a mutualistic model, Nonlinear Anal. RWA, 11 (2010), 3421-3430.
doi: 10.1016/j.nonrwa.2009.12.002. |
[6] |
V. A. Galaktionov and J. L. Vazquez, The problem of blow-up in nonlinear parabolic equations, Discrete Contin. Dyn. Syst., 8 (2002), 399-433.
doi: 10.3934/dcds.2002.8.399. |
[7] |
K. Kim and Z. Lin, A degenerate parabolic system with self-diffusion for a mutualistic model in ecology, Nonlinear Anal. RWA, 7 (2006), 597-609.
doi: 10.1016/j.nonrwa.2005.03.020. |
[8] |
O. A. Ladyzenskaja, V. A. Solonnikov and N. N. Uralceva, Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc., Providence, 1967. |
[9] |
C. Mu, X. Hu, Y. Li and Z. Cui, Blow-up and global existence for a coupled system of degenerte parabolic equations in a bounded domain, Acta Math. Sci., 27B (2007), 92-106.
doi: 10.1016/S0252-9602(07)60008-3. |
[10] |
C. V. Pao, A Lotka-Volterra cooperating reaction-diffusion system with degenerate density-dependent diffusion, Nonl. Anal., 95 (2014), 460-467.
doi: 10.1016/j.na.2013.09.015. |
[11] |
C. V. Pao, Dynamics of Lotka-Volterra competition reaction-diffusion systems with degenerate diffusion, J. Math. Anal. Appl., 421 (2015), 1721-1742.
doi: 10.1016/j.jmaa.2014.07.070. |
[12] |
C. V. Pao and W. H. Ruan, Quasilinear parabolic and elliptic systems with mixed quasimonotone functions, J. Differential Equations, 255 (2013), 1515-1553.
doi: 10.1016/j.jde.2013.05.015. |
[13] |
M. Wang, Some degenerate and quasilinear parabolic systems not in divergence form, J. Math. Anal. Appl., 274 (2002), 424-436.
doi: 10.1016/S0022-247X(02)00347-5. |
[14] |
M. Wang and C. Xie, A degenerate and strongly coupled quasilinear parabolic system not in divergence form, Z. Angew. Math. Phys., 55 (2004), 741-755.
doi: 10.1007/s00033-004-1133-4. |
[15] |
W. Yang, J. Wu and H. Nie, Some uniqueness and multiplicity results for a predator-prey dynamics with a nonlinear growth rate, Commun. Pure Appl. Anal., 14 (2015), 1183-1204.
doi: 10.3934/cpaa.2015.14.1183. |
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