Publications Arnd Scheel

Publications - Arnd Scheel

Preprints

Refereed Journals

Review Articles

Proceedings

Theses

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Preprints

A. Scheel: Robustness of Liesegang patterns (PDF)
T. Gallay, A. Scheel: Diffusive stability of oscillations in reaction-diffusion systems (PDF)

Refereed Journals

A. Scheel, E. van Vleck: Lattice differential equations embedded into reaction-diffusion systems (PDF)
Proc. Royal Soc. Edinburgh A, to appear.
A. Doelman, B. Sandstede, A. Scheel, G. Schneider: The dynamics of modulated wave trains (PDF)
Memoirs of the AMS, to appear.
J.D. Wright, A. Scheel: Colliding dissipative pulses - the shooting manifold (PDF)
J. Differential Eqns. 245 (2008), 59-79.
B. Sandstede, A. Scheel: Hopf bifurcation from viscous shock waves (PDF)
SIAM J. Math. Anal. 39 (2008), 2033-2052.
B. Sandstede, A. Scheel: Relative Morse indices, Fredholm indices, and group velocities (PDF)
Discr. Cont. Dyn. Sys. 20 (2008), 139-158.
M. Haragus, A. Scheel: Interfaces between rolls in the Swift-Hohenberg equation (PDF)
Int. J. Dyn. Sys. Diff. Eqns. 1 (2007), 89-97.
J.D.M. Rademacher, A. Scheel: Instabilities of wave trains and Turing patterns in large domains (PDF )
Int. J. Bif. Chaos 16 (2007), 2679-2691.
J.D. Wright, A. Scheel: Solitary waves and their linear stability in weakly coupled KdV equations (PDF)
Z. Angew. Math. Phys. 58 (2007), 535-570.
B. Sandstede, A. Scheel: Period-doubling of spiral waves and defects (PDF)
SIAM J. Appl. Dyn. Syst. 6 (2007), 494-547.
M. Haragus, A. Scheel: Stable viscous shocks in elliptic conservation laws (Postscript , PDF)
Indiana Univ. Math. J. 56 (2007), 1261-1278.
J.D.M. Rademacher, A. Scheel: The saddle-node of nearly homogeneous wave trains in reaction-diffusion systems (Postscript , PDF)
J. Dyn. Diff. Eqns. 19 (2007), 479-496.
J.D.M. Rademacher, B. Sandstede, A. Scheel: Computing absolute and essential spectra using continuation (PDF)
Physica D 229 (2007), 166-183.
R. Kollár, A. Scheel: Coherent structures generated by inhomogeneities in oscillatory media (PDF)
SIAM J. Appl. Dyn. Syst. 6 (2007), 236-262.
M. Haragus, E. Lombardi, A. Scheel: Spectral stability of wave trains in the Kawahara equation (Postscript , PDF)
J. Math. Fluid Mechanics 8 (2006), 482-509.
A. Scheel: Coarsening fronts (Postscript , PDF)
Archive for Rational Mechanics and Analysis 181 (2006), 505-534.
M. Haragus, A. Scheel: Almost planar waves in anisotropic media (Postscript , PDF)
Comm. Partial Differential Equations 31 (2006), 791-815.
M. Haragus, A. Scheel: Corner defects in almost planar interface propagation (Postscript , PDF)
Ann. Inst. H. Poincare (C) Anal. Non Lineaire 23 (2006), 283-329.
B. Sandstede and A. Scheel: Curvature effects on spiral spectra: Generation of point eigenvalues near branch points (Postscript , PDF)
Phys. Rev. E 73 (2006), 016217.
B. Sandstede, A. Scheel: Basin boundaries and bifurcations near convective instabilities: A case study (Postscript , PDF)
J. Diff. Eqns. 208 (2005), 176-193.
B. Sandstede, A. Scheel: Absolute instabilities of standing pulses (Postscript , PDF)
Nonlinearity 18 (2005), 331-378.
B. Sandstede, A. Scheel: Evans function and blow-up methods in critical eigenvalue problems (Postscript , PDF)
Discr. Cont. Dyn. Sys. 10 (2004), 941-964.
B. Sandstede, A. Scheel: Defects in oscillatory media: toward a classification (Postscript , PDF)
SIAM J. Appl. Dyn. Syst. 3 (2004), 1-68.
A. Scheel: Radially symmetric patterns of reaction-diffusion systems (Postscript, PDF)
Mem. Amer. Math. Soc. 165 (2003).
D.Pelinovsky, A. Scheel: Stability analysis of stationary light transmission in nonlinear photonic structures (Postscript , PDF)
J. Nonlinear Science 13 (2003), 347-396.
A. Doelman, B. Sandstede, A. Scheel, and G. Schneider: Propagation of hexagonal patterns near onset (Postscript, PDF)
Europ. J. Appl. Math. 14 (2003), 85-110.
K. Matthies, A. Scheel: Exponential Averaging for Hamiltonian Evolution Equations (Postscript, PDF)
Trans. Amer. Math. Soc. 355 (2003), 747-773.
J. Härterich, B. Sandstede, A. Scheel: Exponential dichotomies for non-autonomous functional differential equations of mixed type (Postscript , PDF)
Indiana Univ. Math. J. 51 (2002), 1081-1109.
M. Haragus, A. Scheel: Linear stability and instability of ion-acoustic plasma solitary waves (Postscript, PDF)
Physica D 170 (2002), 13-30.
M. Haragus, A. Scheel: Finite-wavelength stability of capillary-gravity solitary waves (Postscript, PDF)
Commun. Math. Phys. 225 (2002), 487-521.
B. Sandstede, A. Scheel: On the structure of spectra of modulated travelling waves (Postscript, PDF)
Math. Nachr. 232 (2001), 39-93.
B. Sandstede, A. Scheel: Super-spiral structures of meandering and drifting spiral waves
Phys. Rev. Lett. 86 (2001), 171-174.
B. Sandstede, A. Scheel: On the stability of periodic travelling waves with large spatial period
J. Diff. Eqns. 172 (2001), 134-188.
B. Sandstede, A. Scheel: Essential instabilities of fronts: bifurcation and bifurcation failure
Dynamical Systems 16 (2001), 1-28.
B. Sandstede, A. Scheel: Absolute versus convective instability of spiral waves
Phys. Rev. E. 62 (2000), 7708-7714.
B. Sandstede, A. Scheel: Absolute and convective instabilities of waves on unbounded and large bounded domains
Physica D 145 (2000), 233-277.
B. Sandstede, A. Scheel: Gluing unstable fronts and backs together can produce stable pulses
Nonlinearity 13 (2000), 1465-1482.
B. Sandstede, A. Scheel: Spectral stability of modulated travelling waves bifurcating near essential instabilities
Proc. Roy. Soc. Edinb. A 130 (2000), 419-448.
G. J. Lord, D. Peterhof, B. Sandstede, A. Scheel: Numerical computation of solitary waves in infinite cylindrical domains
SIAM J. Numerical Analysis 37 (2000), 1420-1454.
B. Sandstede, A. Scheel: Essential instability of pulses and bifurcations to modulated travelling waves
Proc. Roy. Soc. Edinb. A 129 (1999), 1263-1290.
B. Sandstede, A. Scheel, C. Wulff: Bifurcations and dynamics of spiral waves
J. Nonlinear Science 9 (1999), 439-478.
B. Fiedler, A. Scheel, M.I. Vishik: Large patterns of elliptic systems in infinite cylinders
J. Math. Pures Appl. 77 (1998), 879-907.
A. Scheel: Bifurcation to spiral waves in reaction-diffusion systems
SIAM J. Math. Anal. 29 (1998), 1399-1418.
A. Scheel: Subcritical bifurcation to infinitely many rotating waves
J. Math. Anal. Appl. 215 (1997), 252-261.
B. Sandstede, A. Scheel, C. Wulff: Dynamics of spiral waves on unbounded domains using center-manifold reduction
J. Diff. Eqns. 141 (1997), 122-149.
D. Peterhof, B. Sandstede, A. Scheel: Exponential dichotomies for solitary wave solutions of semilinear elliptic equations on infinite cylinders
J. Diff. Eqns. 140 (1997), 266-308.
B. Sandstede, A. Scheel, C. Wulff: Center manifold reduction for spiral wave dynamics
C. R. Acad. Sci. Paris, Serie I, t.324 (1997), 153-158.
P. Chossat, M. Krupa, I. Melbourne, A. Scheel: Transverse bifurcations of homoclinic cycles
Physica D 100 (1997) 85-100.
A. Scheel: Existence of fast travelling waves for some parabolic equations --- a dynamical systems approach.
J. Dyn. Diff. Eqns. 8 (1996), 469-548.
B. Fiedler, B. Sandstede, A. Scheel, C. Wulff: Bifurcation from relative equilibria of noncompact group actions: skew products, meanders, and drifts (Postscript, PDF)
Documenta Mathematica 1 (1996), 479-505.
B. Sandstede ,A. Scheel: Forced symmetry breaking of homoclinic cycles
Nonlinearity 8 (1995), 333-365.
A. Scheel: Fast travelling waves for convective reaction-diffusion equations
C. R. Acad. Sci. Paris, Serie I, t. 317 (1993), 347-351.
A. Scheel: Fast travelling waves for the Cahn-Hilliard equation in an infinite strip
C. R. Acad. Sci. Paris, Serie I, t. 317 (1993), 261-265.
A. Scheel, P. Chossat: Bifurcation d'orbites periodiques a partir d'un cycle homocline symetrique
C. R. Acad. Sci. Paris, Serie I, t. 314 (1992), 49-54.

Review Articles

M. Haragus, A. Scheel: A bifurcation approach to non-planar traveling waves in reaction-diffusion systems (Postscript , PDF)
GAMM-Mitt. 30, (2007), 75-95.
B. Fiedler, A. Scheel: Spatio-Temporal Dynamics of Reaction-Diffusion Patterns (Postscript, PDF)
In Trends in Nonlinear Analysis, M. Kirkilionis, S. Krömker, R. Rannacher, F. Tomi (Eds.), Springer-Verlag, Berlin, 2003 (145 pages).
B. Sandstede, A. Scheel, C. Wulff: Dynamical behavior of patterns with euclidean symmetry
In ``Pattern formation in continuous and coupled systems'', M. Golubitsky, D. Luss and S. Strogatz (eds.), Springer-Verlag. IMA Volumes in Mathematics and its Applications 115 (1999), 249-264.

Proceedings

B. Sandstede, A. Scheel: Absolute and convective stability in large domains
In Proceedings of Equadiff 99, B. Fiedler, K. Gröoger, and J. Sprekels (eds.), World Scientific Publishing, Singapore (2000), 797-800.
M. Efendiev, A. Scheel: Upper and lower bounds for the Hausdorff dimension of the attractor for reaction-diffusion equations in R\sup n
In Proceedings of ``Nonlinear evolution equations and application'', M.Otani (ed.), RIMS, Kyoto (1999), 81-90.
P. Chossat, M. Krupa, I. Melbourne, A. Scheel: Magnetic dynamos in rotating convection --- a dynamical systems approach
Dyn. Cont. Discrete Impulsive Syst. 5 (1999), 327-340.
A. Scheel: Meandering Spirals
Z. Angew. Math. Mech. 79 (1999) 163-166.

Theses

DEA INLN, Nice 1991: Bifurcation d'orbites periodiques a partir de cycles homoclines en presence de symetrie
PhD, FU Berlin, 1994: Existence of fast travelling waves for some parabolic equations - a dynamical systems approach
Habilitation, FU Berlin, 2001: Radially symmetric patterns of reaction-diffusion systems

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