[1]
|
Amann, H. (1990) Dynamic Theory of Quasilinear Parabolic Systems II. Reaction-Diffusion Systems, Differential Integral Equations, 3, 13-75.
|
[2]
|
Aronson, D.G., Crandall, M.G. and Peletier, L.A. (1982) Stabilization of Solutions oa a Degenerate Nonlinear Diffusion Problem. Nonlinear Analysis, 6, 1001-1022. http://dx.doi.org/10.1016/0362-546X(82)90072-4
|
[3]
|
Constantin, A., Escher, J. and Yin, Z. (2004) Global Solutions for Quasilinear Parabolic Systems. Journal of Differential Equations, 197, 73-84. http://dx.doi.org/10.1016/S0022-0396(03)00165-7
|
[4]
|
Ladyzenskaja, O.A., Solonnikov, V.A. and Ural’ceva, N.N. (1968) Linear and Quasi-Linear Equations of Parabolic Type. Transactions of the American Mathematical Society, Monographs 23, Providence.
|
[5]
|
Pao, C.V. (2007) Quasilinear Parabolic and Elliptic Equations with Nonlinear Boundary Conditions. Nonlinear Analysis, 66, 639-662. http://dx.doi.org/10.1016/j.na.2005.12.007
|
[6]
|
Zhang, Q.Y. and Lin, Z.G. (2010) Periodic Solutions of Quasilinear Parabolic Systems with Nonlinear Boundary Conditions. Nonlinear Analysis, 72, 3429-3435. http://dx.doi.org/10.1016/j.na.2009.12.026
|
[7]
|
Crooks, E.C.M., Dancer, E.N., Hilhorst, D., Mimura, M. and Ninomiya, H. (2004) Spatial Segregation Limit of a Competition Diffusion System with Dirichlet Boundary Conditions. Nonlinear Analysis: Real World Applications, 5, 645-665. http://dx.doi.org/10.1016/j.nonrwa.2004.01.004
|
[8]
|
Dancer, E.N. and Du, Y.H. (1994) Competing Species Equations with Diffusion, Large Interactions, and Jumping Nonlinearities. Journal of Differential Equations, 114, 434-475. http://dx.doi.org/10.1006/jdeq.1994.1156
|
[9]
|
Dancer, E.N., Hilhorst, D., Mimura, M. and Peletier, L.A. (1999) Spatial Segregation Limit of a Competition-Diffusion System. European Journal of Applied Mathematics, 10, 97-115.
|
[10]
|
Dancer, E.N., Wang, K. and Zhang, Z. (2012) The Limit Equation for the Gross-Pitaevskii Equations and S. Terracini’s Conjecture. Journal of Functional Analysis, 262, 1087-1131. http://dx.doi.org/10.1016/j.jfa.2011.10.013
|
[11]
|
Namba, T. and Mimura, M. (1980) Spatial Distribution for Competing Populations. Journal of Theoretical Biology, 87, 795-814. http://dx.doi.org/10.1016/0022-5193(80)90118-6
|
[12]
|
Shigesada, N., Kawasaki, K. and Teramoto, E. (1979) Spatial Segregation of Interacting Species. Journal of Theoretical Biology, 79, 83-99. http://dx.doi.org/10.1016/0022-5193(79)90258-3
|
[13]
|
Wang, K.L. and Zhang, Z.T. (2010) Some New Results in Competing Systems with Many Species. Annales de l’Institut Henri Poincare (C) Non Linear Analysis, 27, 739-761. http://dx.doi.org/10.1016/j.anihpc.2009.11.004
|
[14]
|
Wei, J.C. and Weth, T. (2008) Asymptotic Behaviour of Solutions of Planar Elliptic Systems with Strong Competition. Nonlinearity, 21, 305-317. http://dx.doi.org/10.1088/0951-7715/21/2/006
|
[15]
|
Zhang, S., Zhou, L., Liu, Z.H. and Lin, Z.G. (2012) Spatial Segregation Limit of a Non-Autonomous Competition-Diffusion System. Journal of Mathematical Analysis and Applications, 389, 119-129.
http://dx.doi.org/10.1016/j.jmaa.2011.11.054
|
[16]
|
Caffarelli, L.A., Karakhanyan, A.L. and Lin, F.H. (2009) The Geometry of Solutions to a Segregation Problem for Nondivergence Systems. Journal of Fixed Point Theory and Applications, 5, 319-351.
http://dx.doi.org/10.1007/s11784-009-0110-0
|
[17]
|
Dancer, E.N., Wang, K.L. and Zhang, Z.T. (2011) Uniform Hölder Estimate for Singularly Perturbed Parabolic Systems of Bose-Einstein Condensates and Competing Species. Journal of Differential Equations, 251, 2737-2769.
http://dx.doi.org/10.1016/j.jde.2011.06.015
|
[18]
|
Conti, M., Terracini, S. and Verzini, G. (2005) Asymptotic Estimates for the Spatial Segregation of Competitive Systems. Advances in Mathematics, 195, 524-560. http://dx.doi.org/10.1016/j.aim.2004.08.006
|
[19]
|
Zhang, S., Zhou, L. and Liu, Z.H. (2013) The Spatial Behavior of a Competition Diffusion Advection System with Strong Competition. Nonlinear Analysis: Real World Applications, 14, 976-989.
http://dx.doi.org/10.1016/j.nonrwa.2012.08.011
|
[20]
|
Chang, S.M., Lin, C.S., Lin, T.C. and Lin, W.W. (2004) Segregated Nodal Domains of Two-Dimensional Multispecies Bose-Einstein Condensates. Physica D: Nonlinear Phenomena, 196, 341-361.
http://dx.doi.org/10.1016/j.physd.2004.06.002
|
[21]
|
Noris, B., Tavares, H., Terracini, S. and Verzini, G. (2010) Uniform Hölder Bounds for Nonlinear Schrödinger Systems with Strong Competition. Communications on Pure and Applied Mathematics, 63, 267-302.
|
[22]
|
Soave, N. and Zilio, A. (2015) Uniform Bounds for Strongly Competing Systems: The Optimal Lipschitz Case. Archive for Rational Mechanics and Analysis, 218, 647-697. http://dx.doi.org/10.1007/s00205-015-0867-9
|
[23]
|
Caffarelli, L.A. and Lin, F.H. (2008) Singularly Perturbed Elliptic Systems and Multi-Valued Harmonic Functions with Free Boundaries. Journal of the American Mathematical Society, 21, 847-862.
http://dx.doi.org/10.1090/S0894-0347-08-00593-6
|
[24]
|
Tavares, H. and Terracini, S. (2012) Regularity of the Nodal Set of Segregated Critical Configurations under a Weak Reflection Law. Calculus of Variations and Partial Differential Equations, 45, 273-317.
http://dx.doi.org/10.1007/s00526-011-0458-z
|
[25]
|
Caffarelli, L.A. and Lin, F. (2010) Analysis on the Junctions of Domain Walls. Discrete and Continuous Dynamical Systems, 28, 915-929.
|
[26]
|
Zhang, S. and Liu, Z.H. (2015) Singularities of the Nodal Set of Segregated Configurations. Calculus of Variations and Partial Differential Equations, 54, 2017-2037. http://dx.doi.org/10.1007/s00526-015-0854-x
|
[27]
|
Evans, L.C. (1998) Partial Differential Equations. Graduate Studies in Mathematics, Vol. 19, American Mathematical Society, Providence.
|
[28]
|
Dibenedetto, E. (1993) Degenerate Parabolic Equations. Springer-Verlag, New York.
http://dx.doi.org/10.1007/978-1-4612-0895-2
|
[29]
|
Gilbarg, D. and Trudinger, N.S. (2001) Elliptic Partial Differential Equations of Second Order. 2nd Edition, Springer, New York.
|