@article{AIHPC_2006__23_3_283_0,
author = {Haragus, Mariana and Scheel, Arnd},
title = {Corner defects in almost planar interface propagation},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {283--329},
year = {2006},
publisher = {Elsevier},
volume = {23},
number = {3},
doi = {10.1016/j.anihpc.2005.03.003},
mrnumber = {2217654},
zbl = {1098.35085},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.anihpc.2005.03.003/}
}
TY - JOUR AU - Haragus, Mariana AU - Scheel, Arnd TI - Corner defects in almost planar interface propagation JO - Annales de l'I.H.P. Analyse non linéaire PY - 2006 SP - 283 EP - 329 VL - 23 IS - 3 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.anihpc.2005.03.003/ DO - 10.1016/j.anihpc.2005.03.003 LA - en ID - AIHPC_2006__23_3_283_0 ER -
%0 Journal Article %A Haragus, Mariana %A Scheel, Arnd %T Corner defects in almost planar interface propagation %J Annales de l'I.H.P. Analyse non linéaire %D 2006 %P 283-329 %V 23 %N 3 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.anihpc.2005.03.003/ %R 10.1016/j.anihpc.2005.03.003 %G en %F AIHPC_2006__23_3_283_0
Haragus, Mariana; Scheel, Arnd. Corner defects in almost planar interface propagation. Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006) no. 3, pp. 283-329. doi: 10.1016/j.anihpc.2005.03.003
[1] , , , A topological invariant arising in the stability analysis of travelling waves, J. Reine Angew. Math. 410 (1990) 167-212. | Zbl | MR
[2] , , , , , Viscosity Solutions and Applications, Lecture Notes in Math., vol. 1660, Springer-Verlag, Berlin, 1997. | MR
[3] , , Existence of nonplanar solutions of a simple model of premixed Bunsen flames, SIAM J. Math. Anal. 31 (1999) 80-118. | Zbl | MR
[4] , Electron-Steam Interaction with Plasmas, MIT Press, Cambridge, 1964.
[5] , The bifurcations of separatrix contours and chaos, Physica D 62 (1993) 290-299. | Zbl | MR
[6] , , Convergence of the phase field model to its sharp interface limits, Eur. J. Appl. Math. 9 (1998) 417-445. | Zbl | MR
[7] , , , Traveling wave solutions for systems of ODEs on a two-dimensional spatial lattice, SIAM J. Appl. Math. 59 (1999) 455-493. | Zbl | MR
[8] , , On the semi-classical limit for the focusing nonlinear Schrödinger equation: sensitivity to analytic properties of the initial data, Proc. Roy. Soc. London Ser. A (2002) 135-156. | Zbl | MR
[9] , , , , Dividing blobs, chemical flowers and patterned islands in a reaction-diffusion system, J. Chem. Phys. 102 (1998) 8236-8244.
[10] , , , , Propagation of hexagonal patterns near onset, Eur. J. Appl. Math. 14 (2003) 85-110. | Zbl | MR
[11] A. Doelman, B. Sandstede, A. Scheel, G. Schneider, The dynamics of modulated wave trains, Preprint, 2004.
[12] , Asymptotic stability of travelling wave solutions for perturbations with algebraic decay, J. Differential Equations 185 (2002) 348-369. | Zbl | MR
[13] E. Eszter, Evans function analysis of the stability of periodic travelling wave solutions of the FitzHugh-Nagumo system, PhD Thesis, University of Massachusetts at Amherst, 1999.
[14] , , , , Bifurcation from relative equilibria of noncompact group actions: skew products, meanders, and drifts, Documenta Math. 1 (1996) 479-505. | Zbl | MR
[15] , Dynamics of internal layers and diffusive interfaces, CBMS-NSF Regional Conf. Ser. in Appl. Math., vol. 53, SIAM, Philadelphia, PA, 1988. | Zbl | MR
[16] , , The gap lemma and geometric criteria for instability of viscous shock profiles, Comm. Pure Appl. Math. 51 (1998) 797-855. | Zbl | MR
[17] , , , Traveling and spiral waves for sequential flames with translation symmetry: coupled CGL-Burgers equations, Physica D 160 (2001) 1-28. | Zbl | MR
[18] , , , Stability and instability in the Gray-Scott model: the case of equal diffusivities, Appl. Math. Lett. 12 (1999) 59-65. | Zbl | MR
[19] , , , Exact homoclinic and heteroclinic solutions of the Gray-Scott model for autocatalysis, SIAM J. Appl. Math. 61 (2000) 102-130. | Zbl | MR
[20] , , Solutions of semilinear elliptic equations in with conical-shaped level sets, Comm. Partial Differential Equations 25 (2000) 769-819. | Zbl | MR
[21] , , , Stability of travelling waves in a model for conical flames in two space dimensions, Ann. Sci. École Norm. Sup. (4) 37 (2004) 469-506. | Zbl | MR | Numdam
[22] , , Shock structures and bunching fronts in excitable reaction-diffusion systems, Phys. Rev. E 65 (2002) 046224.
[23] , , Breaking the dimension of a steady wave: some examples, in: Nonlinear Dynamics and Pattern Formation in the Natural Environment, Pitman Res. Notes Math. Ser., vol. 335, Longman, Harlow, 1995, pp. 119-129. | Zbl | MR
[24] , , Breaking the dimension of solitary waves, in: Progress in Partial Differential Equations: The Metz Surveys, 4, Pitman Res. Notes Math. Ser., vol. 345, Longman, Harlow, 1996, pp. 216-228. | Zbl | MR
[25] , , , Pattern formation in restricted geometries: the NO + CO reaction on Pt(100), J. Chem. Phys. 112 (2000) 6795-6803.
[26] , On the existence of homoclinic and periodic orbits for the FitzHugh-Nagumo equations, Quart. J. Math. Oxford Ser. 27 (1976) 123-134. | Zbl | MR
[27] , Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math., vol. 804, Springer-Verlag, New York, 1981. | Zbl | MR
[28] , , Asymptotic behavior of multidimensional scalar viscous shock fronts, Indiana Univ. Math. J. 49 (2000) 427-474. | Zbl | MR
[29] , , Internal layers intersecting the boundary of domain in the Allen-Cahn equation, Japan J. Indust. Appl. Math. 18 (2001) 697-738. | Zbl | MR
[30] , , , Dynamics of patterns of chemical reactions on surfaces, in: Evolution of Spontaneous Structures in Dissipative Continuous Systems, Lecture Notes in Phys., vol. 55, Springer, Berlin, 1998, pp. 384-410. | Zbl
[31] , , Topics in Bifurcation Theory and Applications, Adv. Ser. Nonlinear Dynam., vol. 3, World Scientific, River Edge, NJ, 1998. | Zbl | MR
[32] , Stability of the travelling wave solution of the FitzHugh-Nagumo system, Trans. Amer. Math. Soc. 286 (1984) 431-469. | Zbl | MR
[33] , , , Stability of travelling waves for nonconvex scalar viscous conservation laws, Comm. Pure Appl. Math. 46 (1993) 505-526. | Zbl | MR
[34] , , Pulsating wave propagation in reactive flows: flow-distributed oscillations, Phys. Rev. E 61 (2000) 3334-3338.
[35] , On the stability of travelling waves in weighted spaces, J. Differential Equations 112 (1994) 179-215. | Zbl | MR
[36] , Multidimensional stability of planar travelling waves, Trans. Amer. Math. Soc. 349 (1997) 257-269. | Zbl | MR
[37] , , Stability of bright solitary wave solutions to perturbed nonlinear Schrödinger equations, Physica D 124 (1998) 58-103. | Zbl | MR
[38] , , Travelling-waves of the Kuramoto-Sivashinsky equation: period-multiplying bifurcations, Nonlinearity 5 (1992) 899-919. | Zbl | MR
[39] , Wave-solutions of reversible systems and applications, J. Differential Equations 45 (1982) 113-127. | Zbl | MR
[40] , , , Swift-Hohenberg equation for lasers, Phys. Rev. Lett. 73 (1994) 2978-2981.
[41] , , , , , , Advances in the Theory of Shock Waves, Progr. Nonlinear Differential Equations Appl., vol. 47, Birkhäuser, Boston, MA, 2001. | MR
[42] , Oscillatory Integrals and Phenomena beyond all Algebraic Orders. With Applications to Homoclinic Orbits in Reversible Systems, Lecture Notes in Math., vol. 1741, Springer-Verlag, Berlin, 2000. | Zbl | MR
[43] , Quadratic differential equations and non-associative algebras, in: Contributions to the Theory of Nonlinear Oscillations, vol. V, Princeton University Press, Princeton, NJ, 1960, pp. 185-213. | Zbl | MR
[44] , , Pulsations in a burner-stabilized premixed plane flame, SIAM J. Appl. Math. 40 (1981) 551-562. | Zbl | MR
[45] , Reduction of quasilinear elliptic equations in cylindrical domains with applications, Math. Methods Appl. Sci. 10 (1988) 51-66. | Zbl | MR
[46] , , Spatio-temporal chaos for the Gray-Scott model, Physica D 150 (2001) 137-162. | Zbl
[47] , Exponential dichotomies and Fredholm operators, Proc. Amer. Math. Soc. 104 (1988) 149-156. | Zbl | MR
[48] , , Propagation of the hexagonal pattern, Europhys. Lett. 27 (1994) 433-436.
[49] , Invariant manifolds in singular perturbation problems for ordinary differential equations, Proc. Roy. Soc. Edinburgh Sect. A 116 (1990) 45-78. | Zbl | MR
[50] , , Absolute and convective instabilities of waves on unbounded and large bounded domains, Physica D 145 (2000) 233-277. | Zbl | MR
[51] , , On the structure of spectra of modulated travelling waves, Math. Nachr. 232 (2001) 39-93. | Zbl | MR
[52] , , Essential instabilities of fronts: bifurcation and bifurcation failure, Dynamical Systems 16 (2001) 1-28. | Zbl | MR
[53] , , On the stability of periodic travelling waves with large spatial period, J. Differential Equations 172 (2001) 134-188. | Zbl | MR
[54] , , Defects in oscillatory media: toward a classification, SIAM J. Appl. Dyn. Syst. 3 (2004) 1-68. | Zbl | MR
[55] , , , Dynamics of spiral waves on unbounded domains using center-manifold reduction, J. Differential Equations 141 (1997) 122-149. | Zbl | MR
[56] , On the stability of waves of nonlinear parabolic systems, Adv. in Math. 22 (1976) 312-355. | Zbl | MR
[57] , Radially symmetric patterns of reaction-diffusion systems, Mem. Amer. Math. Soc. 165 (2003). | Zbl | MR
[58] , Nonlinear Spatio-Temporal Dynamics and Chaos in Semiconductors, Cambridge Nonlinear Science Series, vol. 10, Cambridge University Press, 2001.
[59] , Nonlinear analysis of hydrodynamic instability in laminar flames I. Derivation of basic equations, Acta Astronautica 4 (1977) 1177-1206. | Zbl | MR
[60] , , , , , Stability properties of traveling pulse solutions of the higher-dimensional FitzHugh-Nagumo equations, Japan J. Appl. Math. 6 (1989) 341-366. | Zbl | MR
[61] , , Singular perturbation theory of traveling waves in excitable media (a review), Physica D 32 (1988) 327-361. | Zbl | MR
[62] , Front propagation into unstable states. II. Linear versus nonlinear marginal stability and rate of convergence, Phys. Rev. A 39 (1989) 6367-6390. | MR
[63] , Front propagation into unstable states, Phys. Rep. 386 (2003) 29-222. | Zbl
[64] , , , Traveling Wave Solutions of Parabolic Systems, Transl. Math. Monographs, vol. 140, American Mathematical Society, Providence, RI, 1994. | Zbl | MR
[65] , Combustion Theory, Benjamin Cummings, Menlo Park, 1985.
[66] , The Geometry of Biological Time, Interdiscip. Appl. Math., vol. 12, Springer-Verlag, New York, 2001. | Zbl | MR
[67] , Stability of fast travelling pulse solutions of the FitzHugh-Nagumo equations, J. Math. Biology 22 (1985) 81-104. | Zbl | MR
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