Curved fronts in the Belousov–Zhabotinskii reaction–diffusion systems in R2

Belousov, 1959, A periodic reaction and its mechanism, Ref. Radiat. Med. Medgiz, 145 Bonnet, 1999, Existence of nonplanar solutions of a simple model of premixed Bunsen flames, SIAM J. Math. Anal., 31, 80, 10.1137/S0036141097316391 Brazhnik, 1995, Non-spiral autowave structures in unrestricted excitable media, Phys. Lett. A, 199, 40, 10.1016/0375-9601(95)00024-W Brazhnik, 2000, On traveling wave solutions of Fisher's equation in two spatial dimensions, SIAM J. Appl. Math., 60, 371, 10.1137/S0036139997325497 Conley, 1984, An application of the generalized Morse index to travelling wave solutions of a competitive reaction–diffusion model, Indiana Univ. Math. J., 33, 319, 10.1512/iumj.1984.33.33018 Friedman, 1964 Field, 1972, Oscillations in chemical systems. II. Thorough analysis of temporal oscillation in the bromate-cerium-malonic acid system, J. Amer. Chem. Soc., 94, 8649, 10.1021/ja00780a001 Field, 1974, Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemical reaction, J. Chem. Phys., 60, 1877, 10.1063/1.1681288 Fife, 1975, The approach of solutions of nonlinear diffusion equations to travelling wave solutions, Bull. Amer. Math. Soc., 81, 1076, 10.1090/S0002-9904-1975-13922-X Gardner, 1982, Existence and stability of travelling wave solutions of competition models: a degree theoretic approach, J. Differential Equations, 44, 343, 10.1016/0022-0396(82)90001-8 Gibbs, 1980, Traveling waves in the Belousov–Zhabotinskii reaction, SIAM J. Appl. Math., 38, 422, 10.1137/0138035 Gilbarg, 2001 Hamel, 2001, Travelling fronts and entire solutions of the Fisher–KPP equation in RN, Arch. Ration. Mech. Anal., 157, 91, 10.1007/PL00004238 Hamel, 2004, Stability of travelling waves in a model for conical flames in two space dimensions, Ann. Sci. Éc. Norm. Supér., 37, 469, 10.1016/j.ansens.2004.03.001 Hamel, 2002, Conical-shaped travelling fronts allied to the mathematical analysis of the shape of premixed Bunsen flames, 169 Hamel, 2005, Existence and qualitative properties of multidimensional conical bistable fronts, Discrete Contin. Dyn. Syst., 13, 1069, 10.3934/dcds.2005.13.1069 Hamel, 2006, Asymptotic properties and classification of bistable fronts with Lipschitz level sets, Discrete Contin. Dyn. Syst., 14, 75 Huang, 2008, Stability of travelling fronts of the Fisher–KPP equation in RN, NoDEA Nonlinear Differential Equations Appl., 15, 599, 10.1007/s00030-008-7041-0 Haragus, 2006, Almost planar waves in anisotropic media, Comm. Partial Differential Equations, 31, 791, 10.1080/03605300500361420 Haragus, 2006, Corner defects in almost planar interface propagation, Ann. Inst. H. Poincaré Anal. Non Linéaire, 23, 283, 10.1016/j.anihpc.2005.03.003 Haragus, 2007, A bifurcation approach to non-planar traveling waves in reaction–diffusion systems, GAMM-Mitt., 30, 75, 10.1002/gamm.200790012 Kanel', 1990, Existence of a travelling wave solution of the Belousov–Zhabotinskii system, Differ. Uravn., 26, 652 Kapel', 1991, Existence of travelling-wave type solutions for the Belousov–Zhabotinskii system of equations, Sib. Math. Zh., 32, 47 Kurokawa, 2011, Multi-dimensional pyramidal travelling fronts in the Allen–Cahn equations, Proc. Roy. Soc. Edinburgh Sect. A, 141, 1031, 10.1017/S0308210510001253 Klaasen, 1981, The asymptotic behavior of solutions of a system of reaction–diffusion equations which models the Belousov–Zhabotinskii chemical reaction, J. Differential Equations, 40, 253, 10.1016/0022-0396(81)90021-8 Liang, 2007, Asymptotic speeds of spread and traveling waves for monotone semiflows with application, Comm. Pure Appl. Math., 60, 1, 10.1002/cpa.20154 Lin, 2009, Travelling wavefronts of Belousov–Zhabotinskii system with diffusion and delay, Appl. Math. Lett., 22, 341, 10.1016/j.aml.2008.04.006 Mischaikow, 1993, Travelling waves for mutualist species, SIAM J. Math. Anal., 24, 987, 10.1137/0524059 Murray, 1977 Murray, 1976, On travelling wave solutions in a model for the Belousov–Zhabotinskii reaction, J. Theoret. Biol., 56, 329, 10.1016/S0022-5193(76)80078-1 Manoranjan, 1982, A numerical study of the Belousov–Zhabotinskii reaction using Galerkin finite element methods, J. Math. Biol., 16, 251 Ni, 2013, Traveling fronts of pyramidal shapes in competition-diffusion systems, Netw. Heterog. Media, 8, 379, 10.3934/nhm.2013.8.379 Ninomiya, 2005, Existence and global stability of traveling curved fronts in the Allen–Cahn equations, J. Differential Equations, 213, 204, 10.1016/j.jde.2004.06.011 Ninomiya, 2006, Global stability of traveling curved fronts in the Allen–Cahn equations, Discrete Contin. Dyn. Syst., 15, 819, 10.3934/dcds.2006.15.819 Quinney, 1979, On computing travelling wave solutions in a model for the Belousov–Zhabotinskii reaction, J. Inst. Math. Appl., 23, 193, 10.1093/imamat/23.2.193 Sattinger, 1971, Monotone methods in nonlinear elliptic and parabolic boundary value problems, Indiana Univ. Math. J., 21, 979, 10.1512/iumj.1972.21.21079 Taniguchi, 2007, Traveling fronts of pyramidal shapes in the Allen–Cahn equations, SIAM J. Math. Anal., 39, 319, 10.1137/060661788 Taniguchi, 2009, The uniqueness and asymptotic stability of pyramidal traveling fronts in the Allen–Cahn equations, J. Differential Equations, 246, 2103, 10.1016/j.jde.2008.06.037 Taniguchi, 2012, Multi-dimensional traveling fronts in bistable reaction–diffusion equations, Discrete Contin. Dyn. Syst., 32, 1011, 10.3934/dcds.2012.32.1011 Taniguchi, 2015, An (N-1)-dimensional convex compact set gives an N-dimensional traveling front in the Allen–Cahn equation, SIAM J. Math. Anal., 47, 455, 10.1137/130945041 Taniguchi, 2016, Convex compact sets in RN−1 give traveling fronts of cooperation-diffusion systems in RN, J. Differential Equations, 260, 4301, 10.1016/j.jde.2015.11.010 Trofimchuk, 2013, Traveling waves for a model of the Belousov–Zhabotinskii reaction, J. Differential Equations, 254, 3690, 10.1016/j.jde.2013.02.005 Trofimchuk, 2014, On the minimal speed of front propagation in a model of the Belousov–Zhabotinskii reaction, Discrete Contin. Dyn. Syst. Ser. B, 19, 1769 Troy, 1980, The existence of traveling wave front solutions of a model of the Belousov–Zhabotinskii chemical reaction, J. Differential Equations, 36, 89, 10.1016/0022-0396(80)90078-9 Pérez-Muñuzuri, 1995, V-shaped stable nonspiral patterns, Phys. Rev. E, 51, 845, 10.1103/PhysRevE.51.R845 Volpert, 1991, Application of the theory of the rotation of vector fields to the investigation of wave solutions of parabolic equations, Trans. Moscow Math. Soc., 1990, 59 Volpert, 1994, Traveling Wave Solutions of Parabolic Systems, vol. 140 Wang, 2012, Traveling curved fronts in monotone bistable systems, Discrete Contin. Dyn. Syst., 32, 2339, 10.3934/dcds.2012.32.2339 Wang, 2016, Nonplanar traveling fronts in reaction–diffusion equations with combustion and degenerate Fisher–KPP nonlinearities, J. Differential Equations, 260, 6405, 10.1016/j.jde.2015.12.045 Wang, 2016, Existence, uniqueness and stability of pyramidal traveling fronts in reaction–diffusion systems, Sci. China Math., 59, 1869, 10.1007/s11425-016-0015-x Wang, 2017, On the existence of axisymmetric traveling fronts in Lotka–Volterra competition-diffusion systems in R3, Discrete Contin. Dyn. Syst. Ser. B, 22, 1111 Wang, 1994, Explicit wave front solutions of Noyes–Field systems for the Belousov–Zhabotinskii reaction, J. Math. Anal. Appl., 182, 705, 10.1006/jmaa.1994.1114 Protter, 1984 Xin, 1992, Multidimensional stability of traveling waves in a bistable reaction–diffusion equation I, Comm. Partial Differential Equations, 17, 1889, 10.1080/03605309208820907 Ye, 1987, Travelling wave front solutions of Noyes–Field system for Belousov–Zhabotinskii reaction, Nonlinear Anal., 11, 1289, 10.1016/0362-546X(87)90046-0 Ye, 1989, A note on traveling wave solutions for Belousov–Zhabotinskii chemical reaction, J. Beijing Inst. Technol., 4, 5 Zaikin, 1970, Concentration wave propagation in two-dimensional liquid-phase self-oscillating system, Nature, 225, 535, 10.1038/225535b0