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On the viscous CahnHilliardNavierStokes equations with dynamic boundary conditions
Nonexistence of traveling wave solutions, exact and semiexact traveling wave solutions for diffusive LotkaVolterra systems of three competing species
1.  Department of Mathematics, National Taiwan University, and National Center for Theoretical Sciences (Taipei Office), No. 1, Sec. 4, Roosevelt Road, Taipei, 10617 
2.  Department of Mathematics, National Taiwan University, and National Center for Theoretical Sciences (Taipei Office), No. 1, Sec. 4, Roosevelt Road, Taipei, 10617 
References:
[1] 
C.C. Chen, L.C. Hung, M. Mimura, M. Tohma and D. Ueyama, Semiexact equilibrium solutions for threespecies competitiondiffusion systems, Hiroshima Math J., 43 (2013), 176206. 
[2] 
C.C. Chen, L.C. Hung, M. Mimura and D. Ueyama, Exact travelling wave solutions of threespecies competitiondiffusion systems, Discrete Contin. Dyn. Syst. Ser. B, 17 (2012), 26532669. doi: 10.3934/dcdsb.2012.17.2653. 
[3] 
Y.S. Chiou, Travelling wave solutions for reactiondiffusionadvection equations, Master Thesis, Department of Mathematics, National Taiwan University, Taiwan, (2010), 149. 
[4] 
P. de Mottoni, Qualitative analysis for some quasilinear parabolic systems, Institute of Math., Polish Academy Sci., zam, 11 (1979), 190. 
[5] 
N. Fei and J. Carr, Existence of travelling waves with their minimal speed for a diffusing LotkaVolterra system, Nonlinear Anal. Real World Appl., 4 (2003), 503524. doi: 10.1016/S14681218(02)000779. 
[6] 
L.C. Hung, Exact traveling wave solutions for diffusive LotkaVolterra systems of two competing species, Jpn. J. Ind. Appl. Math., 29 (2012), 237251. doi: 10.1007/s1316001200562. 
[7] 
H. Ikeda, Multiple travelling wave solutions of threecomponent systems with competition and diffusion, Methods Appl. Anal., 8 (2001), 479496. 
[8] 
H. Ikeda, Travelling wave solutions of threecomponent systems with competition and diffusion, Math. J. Toyama Univ., 24 (2001), 3766. 
[9] 
H. Ikeda, Global bifurcation phenomena of standing pulse solutions for threecomponent systems with competition and diffusion, Hiroshima Math. J., 32 (2002), 87124. 
[10] 
H. Ikeda, Dynamics of weakly interacting front and back waves in threecomponent systems, Toyama Math. J., 30 (2007), 134. 
[11] 
Y. Kanon, Parameter dependence of propagation speed of travelling waves for competitiondiffusion equations, SIAM J. Math. Anal., 26 (1995), 340363. doi: 10.1137/S0036141093244556. 
[12] 
Y. Kanon, Fisher wave fronts for the LotkaVolterra competition model with diffusion, Nonlinear Anal., 28 (1997), 145164. doi: 10.1016/0362546X(95)00142I. 
[13] 
A. Kolmogoroff, I. Petrovsky and N. Piscounoff, Study of the diffusion equation with growth of the quantity of matter and its application to a biological problem, Bull. Math, 1 (1937), 125. (French) Moscow Univ. 
[14] 
A. W. Leung, X. Hou and W. Feng, Traveling wave solutions for LotkaVolterra system revisited, Discrete Contin. Dyn. Syst. Ser. B, 15 (2011), 171196. doi: 10.3934/dcdsb.2011.15.171. 
[15] 
A. W. Leung, X. Hou, and Y. Li, Exclusive traveling waves for competitive reactiondiffusion systems and their stabilities, J. Math. Anal. Appl., 338 (2008), 902924. doi: 10.1016/j.jmaa.2007.05.066. 
[16] 
R. M. May and W. J. Leonard, Nonlinear aspects of competition between three species, SIAM J. Appl. Math., 29 (1975), 243253. 
[17] 
P. D. Miller, Nonmonotone waves in a three species reactiondiffusion model, Methods Appl. Anal., 4 (1997), 261282. 
[18] 
P. D. Miller, Stability of nonmonotone waves in a threespecies reactiondiffusion model, Proc. Roy. Soc. Edinburgh Sect. A, 129 (1999), 125152. doi: 10.1017/S0308210500027499. 
[19] 
A. Okubo, P. Maini, M. Williamson and J. Murray, On the spatial spread of the grey squirrel in britain, Proceedings of the Royal Society of London. B. Biological Sciences, 238 (1989), 113125. 
[20] 
M. Rodrigo and M. Mimura, Exact solutions of a competitiondiffusion system, Hiroshima Math. J., 30 (2000), 257270. 
[21] 
M. Rodrigo and M. Mimura, Exact solutions of reactiondiffusion systems and nonlinear wave equations, Japan J. Indust. Appl. Math., 18 (2001), 657696. doi: 10.1007/BF03167410. 
show all references
References:
[1] 
C.C. Chen, L.C. Hung, M. Mimura, M. Tohma and D. Ueyama, Semiexact equilibrium solutions for threespecies competitiondiffusion systems, Hiroshima Math J., 43 (2013), 176206. 
[2] 
C.C. Chen, L.C. Hung, M. Mimura and D. Ueyama, Exact travelling wave solutions of threespecies competitiondiffusion systems, Discrete Contin. Dyn. Syst. Ser. B, 17 (2012), 26532669. doi: 10.3934/dcdsb.2012.17.2653. 
[3] 
Y.S. Chiou, Travelling wave solutions for reactiondiffusionadvection equations, Master Thesis, Department of Mathematics, National Taiwan University, Taiwan, (2010), 149. 
[4] 
P. de Mottoni, Qualitative analysis for some quasilinear parabolic systems, Institute of Math., Polish Academy Sci., zam, 11 (1979), 190. 
[5] 
N. Fei and J. Carr, Existence of travelling waves with their minimal speed for a diffusing LotkaVolterra system, Nonlinear Anal. Real World Appl., 4 (2003), 503524. doi: 10.1016/S14681218(02)000779. 
[6] 
L.C. Hung, Exact traveling wave solutions for diffusive LotkaVolterra systems of two competing species, Jpn. J. Ind. Appl. Math., 29 (2012), 237251. doi: 10.1007/s1316001200562. 
[7] 
H. Ikeda, Multiple travelling wave solutions of threecomponent systems with competition and diffusion, Methods Appl. Anal., 8 (2001), 479496. 
[8] 
H. Ikeda, Travelling wave solutions of threecomponent systems with competition and diffusion, Math. J. Toyama Univ., 24 (2001), 3766. 
[9] 
H. Ikeda, Global bifurcation phenomena of standing pulse solutions for threecomponent systems with competition and diffusion, Hiroshima Math. J., 32 (2002), 87124. 
[10] 
H. Ikeda, Dynamics of weakly interacting front and back waves in threecomponent systems, Toyama Math. J., 30 (2007), 134. 
[11] 
Y. Kanon, Parameter dependence of propagation speed of travelling waves for competitiondiffusion equations, SIAM J. Math. Anal., 26 (1995), 340363. doi: 10.1137/S0036141093244556. 
[12] 
Y. Kanon, Fisher wave fronts for the LotkaVolterra competition model with diffusion, Nonlinear Anal., 28 (1997), 145164. doi: 10.1016/0362546X(95)00142I. 
[13] 
A. Kolmogoroff, I. Petrovsky and N. Piscounoff, Study of the diffusion equation with growth of the quantity of matter and its application to a biological problem, Bull. Math, 1 (1937), 125. (French) Moscow Univ. 
[14] 
A. W. Leung, X. Hou and W. Feng, Traveling wave solutions for LotkaVolterra system revisited, Discrete Contin. Dyn. Syst. Ser. B, 15 (2011), 171196. doi: 10.3934/dcdsb.2011.15.171. 
[15] 
A. W. Leung, X. Hou, and Y. Li, Exclusive traveling waves for competitive reactiondiffusion systems and their stabilities, J. Math. Anal. Appl., 338 (2008), 902924. doi: 10.1016/j.jmaa.2007.05.066. 
[16] 
R. M. May and W. J. Leonard, Nonlinear aspects of competition between three species, SIAM J. Appl. Math., 29 (1975), 243253. 
[17] 
P. D. Miller, Nonmonotone waves in a three species reactiondiffusion model, Methods Appl. Anal., 4 (1997), 261282. 
[18] 
P. D. Miller, Stability of nonmonotone waves in a threespecies reactiondiffusion model, Proc. Roy. Soc. Edinburgh Sect. A, 129 (1999), 125152. doi: 10.1017/S0308210500027499. 
[19] 
A. Okubo, P. Maini, M. Williamson and J. Murray, On the spatial spread of the grey squirrel in britain, Proceedings of the Royal Society of London. B. Biological Sciences, 238 (1989), 113125. 
[20] 
M. Rodrigo and M. Mimura, Exact solutions of a competitiondiffusion system, Hiroshima Math. J., 30 (2000), 257270. 
[21] 
M. Rodrigo and M. Mimura, Exact solutions of reactiondiffusion systems and nonlinear wave equations, Japan J. Indust. Appl. Math., 18 (2001), 657696. doi: 10.1007/BF03167410. 
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