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Workgroup Nonlinear Partial Differential Equations

Secretariat
Kollegiengebäude Mathematik (20.30)
Room 3.029

Address
Karlsruher Institut für Technologie
Institut für Analysis
Englerstraße 2
76131 Karlsruhe
Germany

Office hours:
Mon-Fri 10-12, Tue+Thu 14-16

Tel.: +49 721 608 42064

Fax.: +49 721 608 46530

Publications

englisch.pdf

79.
with A. Khrabustovskyi, K. Mnasri, Ch. Stohrer, and C. Rockstuhl: Interface conditions for a metamaterial with strong spatial dispersion. Submitted. http://arxiv.org/abs/1710.03676v1

78.
with A. Khrabustovskyi, K. Mnasri, Ch. Stohrer, and C. Rockstuhl: Beyond local effective material properties for metamaterials. Submitted. http://arxiv.org/abs/1705.10969v1

77.
with A. Contreras and D. E. Pelinovsky: Orbital Stability of Domain Walls in Coupled Gross-Pitaevskii Systems. Submitted. http://arxiv.org/abs/1702.00701

76.
with W. Reichel: A breather construction for a semilinear curl-curl wave equation with radially symmetric coefficients. W. J. Elliptic Parabol. Equ. (2016) 2: 371. doi:10.1007/BF03377410

75.
with K. Tanaka, K. Sekine, M. Kashiwagi, and S. Oishi: Verified numerical computation for semilinear elliptic problems with lack of Lipschitz continuity of the first derivative. Submitted. http://arxiv.org/abs/1607.04619

74.
with A. Khrabustovskyi: Spectral properties of elliptic operators with double-contrast coefficients near a hyperplane. Asymptotic Analysis 98 (2016), pp. 91-130, doi: 10.3233/ASY-161363

73.
with M. Brown, V. Hoang, M. Radosz, and I. Wood: Gap localization of TE-Modes by arbitrarily weak defects. To appear in Journal of the London Mathematical Society.

72.
with Y. Watanabe, K. Nagatou, and M. Nakao: Norm bound computation for inverses of linear operators in Hilbert spaces. Journal of Differential Equations 260 (2016), pp. 6363-6374. doi: 10.1016/j.jde.2015.12.041

71.
with F. Pacella and D. Rütters: A computer-assisted existence proof for Emden's equation on an unbounded L-shaped domain. Communications in Contemporary Mathematics, Vol. 19, No. 2 (2017). http://dx.doi.org/10.1142/S0219199717500055

70.
with Th. Bartsch, T. Dohnal, and W. Reichel: Ground states of a nonlinear curl-curl problem in cylindrically symmetric media. Nonlinear Differ. Equ. Appl. (2016) 23: 52. doi:10.1007/s00030-016-0403-0

69.
with B.M. Brown, V. Hoang, and I. Wood: Spectrum created by line defects in
periodic structures. Mathematische Nachrichten 287, No. 17-18, 1972-1985. doi: 10.1002/mana.201300165

68.
with Y. Watanabe, K. Nagatou, and M. T. Nakao: Verified Computations of Eigenvalue Exclosures for Eigenvalue Problems in Hilbert Spaces. SIAM J. Numer. Anal., Vol. 52, No. 2, 975-992, 2014. doi: 10.1137/120894683

67.
with P. J. McKenna, F. Pacella, and D. Roth: A Computer-Assisted Uniqueness Proof for a Semilinear Elliptic Boundary Value Problem. Inequalities and Applications 2010, International Series of Numerical Mathematics, Vol. 161, Part 1, 31-52, 2012. article

66.
with C. Bandle, A. Gilanyi, and L. Losonczi: Inequalities and Applications 2010 (Dedicated to the Memory of Wolfgang Walter), International Series of Numerical Mathematics, Vol. 161, Springer Basel, 2012. book

65.
with M. Brown, V. Hoang, and I. Wood: On the spectrum of waveguides in planar photonic bandgap structures. Proceedings of the Royal Society of London A, 471: 20140673, http://dx.doi.org/10.1098/rspa.2014.0673

64.
with T. Dohnal, K. Nagatou, and W. Reichel: Interfaces supporting surface gap soliton ground states in the 1D nonlinear Schroedinger equation. Journal of Mathematical Analysis and Applications 407 (2013), pp. 425-435. doi: 10.1016/j.jmaa.2013.05.028

63.
with K. Nagatou, M. T. Nakao, and Y. Watanabe: A computer-assisted stability proof for the Orr-Sommerfeld problem with Poiseuille flow. Nonlinear Theory and Its Applications, IEICE 2, 123-127 (2011).

62.
with K. Nagatou und M. T. Nakao: Eigenvalue excluding for perturbed-periodic one-dimensional Schrödinger operators. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 468, Issue 2138 (2012), pp. 545-562; published online before print 10.2011: doi: 10.1098/rspa.2011.0159; pdf

61.
with T. Dohnal and W. Reichel: Surface gap soliton ground states for the nonlinear Schrödinger equation. Comm. Math. Phys., Volume 308, Issue 2 (2011), 511-542; http://www.springerlink.com/content/j01k11547j2p8083/ - pdf

60.
with W. Dörfler, A. Lechleiter, G. Schneider, and Ch. Wieners: Photonic Crystals: Mathematical Analysis and Numerical Approximation. Birkh"auser, 2010; Oberwolfach Seminars 42.

59.
with T. Dohnal and W. Reichel: Localized modes of the linear periodic Schrödinger operator with a nonlocal perturbation. SIAM J. Math. Anal., Volume 41, Issue 5 (2009), 1967-1993. pdf

58.
mit with B. M. Brown, V. Hoang, I. G. Wood: Floquet-Bloch Theory for Elliptic Problems with Discontinuous Coefficients. In: Spectral theory and analysis, 1–20, Oper. Theory Adv. Appl., 214, Birkhäuser/Springer, Basel, 2011.

57.
with P. J. McKenna, F. Pacella, D. Roth: A Uniqueness Result for a Semilinear Elliptic Problem: A Computer-assisted Proof. J. Differential Equations 247 (2009) 2140-2162; doi:10.1016/j.jde.2009.06.023.

56.
Computer-assisted Proofs for Semilinear Elliptic Boundary Value Problems. Japan Journal for Industrial and Applied Mathematics, Vol. 26, No. 2-3 (2009); doi: 10.1007/BF03186542.

55.
with V. Hoang, Ch. Wieners: A computer-assisted proof for photonic band gaps. Z. angew. Math. Phys. 60 (2009) 1035-1052; 0044-2275/09/061035-18; DOI 10.1007/s00033-008-8021-2; www.birkhauser.ch/ZAMP.

54.
with B. M. Brown, V. Hoang, I.G. Wood: On Spectral Bounds for Photonic Crystal Waveguides. In: Inequalities and Applications (C. Bandle, A. Gilànyi, L. Losonczi, Z. Pales, M. Plum eds.), International Series of Numerical Mathematics, Vol. 157, 23-30 (2009).

53.
with Y. Watanabe, M. T. Nakao: A computer-assisted instability proof for the Orr-Sommerfeld problem with Poiseuille flow. Z. Angew. Math. Mech. 89, No. 1, 5-18 (2009)/DOI 10.1002/zamm.200700158.

52.
Existence and Multiplicity Proofs for Semilinear Elliptic Boundary Value Problems by Computer Assistance. DMV Jahresbericht: JB 110, Heft 1 (2008) 19-54.
Download: emp.ps emp.pdf

51.
mit W. N. Everitt, L. Markus, M. Muzzulini: A continuum of unusual selfadjoint linear partial differential operators.
Journal of Computational and Applied Mathematics 208, 164-175 (2007).

50.
with Ch. Wieners: Numerical enclosures for variational inequalities. Computational Methods in Applied Mathematics, Vol. 7, No. 4, 376-388 (2007).

49.
with B. Breuer, J. Horak, P.J. McKenna: A computer-assisted existence and multiplicity proof for travelling waves in a nonlinearly supported beam.
Submitted
Download: travelling.pdf

48.
with R. C. Brown: An Opial Type Inequality with an Integral Boundary Condition.
To appear in Proc. R. Soc. Lond. A.
Download: opial_type.pdf

47.
with W.N. Everitt, L. Markus: An Unusual Self-Adjoint Linear Partial Differential Operator.
Trans. Amer. Math. Soc. 367, 1303-1324 (2005).
Download: self-adjoint.pdf

46.
with E. B. Davies: Spectral Pollution.
IMA Journal of Numerical Analysis 24, 417-438 (2004).

45.
with B. Breuer, P.J. McKenna: Multiple solutions for a semilinear boundary value problem: a computational multiplicity proof.
J. Differential Equations 195, 243-269 (2003).

44.
with B.M. Brown, W.D. Evans: Titchmarsh-Sims-Weyl theory for Complex Hamiltonian Systems.
Proc. London Math. Soc. (3) 87, 419-450 (2003).
Download: titchmarsh.pdf

43.
with J.-R. Lahmann: A computer-assisted instability proof for the Orr-Sommerfeld equation with Blasius profile.
ZAMM 84, No. 3, 188-204 (2004).
Download: orr-sommerfeld.pdf

42.
with E. Adams: Free Vibrations of Trusses by Fourier Decomposition, and Homotopy Methods for Nonlinear Matrix Eigenvalue Problems, I and II.
J. Math. Anal. Appl. 275, 333-353 (2002) and 276, 64-79 (2002).

41.
with Ch. Wieners: New solutions of the Gelfand problem.
J. Math. Anal. Appl. 269, 588-606 (2002).

40.
with Ch. Wieners: Optimal a priori estimates for interface problems.
Numer. Math. 95, 735-759 (2003).

39.
with P. J. McKenna: Multiple solutions for a semilinear boundary value problem: a computational multiplicity proof.
J. Math. Anal. Appl. 251, No. 2, 710-715 (2000).

38.
with B. Breuer, P.J. McKenna: Inclusions and Existence Proofs for Solutions of a Nonlinear Boundary Value Problem by Spectral Numerical Methods.
Computing Suppl. 15, 61-77 (2001).

37.
with Ch. Hipp: Optimal investment for investors with state dependent income, and for insurers.
Finance and Stochastics, Vol. 7, No. 3, 299-321 (2003).

36.
Safe Numerical Error Bounds for Solutions of Nonlinear Elliptic Boundary Value Problems.
In: Symbolic Algebraic Methods and Verification Methods (Eds.: G. Alefeld, J. Rohn, S. Rump, T. Yamamoto), Springer Wien New York, 195-207 (2001).

35.
with Ch. Hipp: Optimal investment for insurers.
Insurance, Mathematics and Economics 27, 215-228 (2000).

34.
with H. Behnke, U. Mertins, Ch. Wieners: Eigenvalue inclusions via domain decomposition.
Proc. R. Soc. Lond. A. 456, 2717-2730 (2000).

33.
Computer-assisted Enclosure Methods for Elliptic Differential Equations.
Linear Algebra and its Applications 324, 147-187 (2001).

32.
with J. Lahmann: Das Spektrum der Orr-Sommerfeld-Gleichung mit Blasius-Strömungsprofil.
ZAMM 78, Suppl. 3, S987 - S988 (1998).

31.
with B. Breuer: Lösungseinschließungen bei einem nichtlinearen Randwertproblem mittels eines Fourierreihenansatzes.
Internal Report.

30.
with R. M. Redheffer: A Class of Second-order Differential Equations.
J. Differential Equations 154, 454-469 (1999).

29.
with J. Lahmann: On the spectrum of the Orr-Sommerfeld equation on the semi-axis.
Math. Nachr. 216, 145-153 (2000).

28.
with B.M. Brown, D.K.R. McCormack, W.D. Evans: On the spectrum of second order differential operators with complex coeficients.
Proc. Royal Soc. London. A 455, 1235-1257 (1999).

27.
with B.M. Brown, M.S.P. Eastham, D.K.R. McCormack: On a new algorithm for the computation of enclosures for the Titchmarsh-Weyl m-function.
Result. Math. 33, 50-64 (1998).

26.
Eigenvalue Problems for Differential Equations.
In: Wavelets, Multilevel Methods and Elliptic PDEs (Eds.: M. Ainsworth , J. Levesley, M. Marletta, W.A. Light), Clarendon Press, Oxford, 39-83 (1997).

25.
Guaranteed Numerical Bounds for Eigenvalues.
In: Spectral theory and computational methods of Sturm-Liouville problems (Eds.: D. Hinton, P. Schaefer), Marcel Dekker, New York, 313-332 (1997).

24.
Enclosure Methods with Existence Proof for Elliptic Differential Equations. Proceedings zu "General Inequalities 7" (Oberwolfach 1995), International Series of Numerical Mathematics, Vol. 123, 347-368 (1997).

23.
Enclosures for Two-Point Boundary Value Problems near Bifurcation Points.
In: Scientific Computing and Validated Numerics, Proceedings of the International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics SCAN-95, held in Wuppertal, Germany, September 26-29, 1995 (Eds.: G. Alefeld, A. Frommer, B. Lang), Mathematical Research, Volume 90, Akademie Verlag, 265-279 (1996).

22.
Existence Proofs for Elliptic Boundary Value Problems by Numerical Means.
ZAMM 75 SII, S429-S432 (1995).

21.
Lösungseinschließung mit automatischem Existenzbeweis bei elliptischen Randwertproblemen.
In: Jahrbuch Überblicke Mathematik 1995 (Hrsg.: A. Beutelspacher, S.D. Chatterji, U. Kulisch, R. Liedl), Vieweg, Braunschweig, 103 - 124 (1995).

20.
Enclosures for Weak Solutions of Nonlinear Elliptic Boundary Value Problems.
In: Inequalities and Applications (Ed.: Ravi P. Agarwal), World Scientific Series In Applicable Analysis, Vol. 3, 505-521 (1994).

19.
Inclusion Methods for Elliptic Boundary Value Problems.
In: Topics in Validated Computations (Ed.: J. Herzberger), Studies in Computational Mathematics 5, North Holland (Elsevier), Amsterdam, 323 - 379 (1994).

18.
Existence and Enclosure Results for Continua of Solutions of Parameter-Dependent Nonlinear Boundary Value Problems.
Journal of Computational and Applied Mathematics 60, 187 - 200 (1995).

17.
with B. Kalkofen: Optimal Pricing Rules for Private-Value Auctions with Incomplete Information.
Ifo-Studien 1/1996, 77 - 100.

16.
Enclosures for Solutions of Parameter-dependent Nonlinear Elliptic Boundary Value Problems: Theory and Implementation on a Parallel Computer.
Interval Computations 3 (Special Issue on Parallel Algorithms), 106 - 121 (1994).

15.
with B.M. Brown, W.D. Evans und V.G. Kirby: Safe numerical bounds for the Titchmarsh-Weyl m-function.
Mathematical Proceedings of the Cambridge Philosophical Society 113, 583-599 (1993).

14.
An Existence and Inclusion Method for Two-Point Boundary Value Problems with Turning Points.
ZAMM 74, 615 - 623 (1994).

13.
Numerical Existence Proofs and Explicit Bounds for Solutions of Nonlinear Elliptic Boundary Value Problems.
Computing 49, 25-44 (1992).

12.
Characterization and Computation of Nash-Equilibria for Auctions with Incomplete Information.
International Journal of Game Theory 20, 393-418 (1992).

11.
Continuous Sealed-bid Auctions with Asymmetric Incomplete Information.
Methods of Operations Research 63, 303-312.

10.
Bounds for eigenvalues of second-order elliptic differential operators.
ZAMP 42, 848 - 863 (1991).

9.
Existence proofs in combination with error bounds for approximate solutions of weakly nonlinear second-order elliptic boundary value problems.
ZAMM 71, T 660 - T 662 (1991).

8.
Explicit H2-estimates and pointwise bounds for solutions of second-order elliptic boundary value problems.
J. Math. Anal. Appl. 165, 36-61 (1992).

7.
Computer-assisted existence proofs for two-point boundary value problems.
Computing 46, 19-34 (1991).

6.
Verified existence and inclusion results for two-point boundary value problems.
IMACS Annals on Computing and Applied Mathematics, Baltzer, Vol. 7, 341-355 (1990).

5.
with M. Göhlen und J. Schröder: A Programmed Algorithm for Existence Proofs for Two-Point Boundary Value Problems.
Computing 44, 91-132 (1990).

4.
Existence and inclusion for two-point boundary value problems by numerical means.
In: Computational Ordinary Differential Equations (Eds.: J. R. Cash, I. Gladwell), Clarendon Press, Oxford, 415-423 (1992).

3.
Eigenvalue inclusions for second-order ordinary differential operators by a numerical homotopy method.
ZAMP 41, 205-226 (1990).

2.
Shape-Invariant Bounds for Reaction-Diffusion Systems with Unequal Diffusion Coeficients.
J. Differential Equations 73, 82-103 (1988).

1.
Pointwise Bounds for Linear Reaction-Diffusion Systems and an Extension to Nonlinear Problems.
J. Math. Anal. Appl. 135, 88-111 (1988).