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Nachwuchsgruppe "Nichtlineare Helmholtzgleichungen"

Dies ist die Seite der Nachwuchsgruppe "Nichtlineare Helmholtzgleichungen", die seit dem 01.07.2016 als assoziiertes Projekt (AP2) dem Sonderforschungsbereich 1173 angegliedert ist. Für eine Beschreibung unserer Forschungsziele und erzielten Resultate verweise ich auf diese Seite.


Personen in der Nachwuchsgruppe Nichtlineare Helmholtzgleichungen
Name Tel. E-Mail
0721 608 46178 rainer.mandel@kit.edu
0721 608 42046 zois.moitier@kit.edu

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Sommersemester 2021 Vorlesung
Wintersemester 2020/21 Seminar
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Wintersemester 2017/18 Vorlesung
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Sommersemester 2017 Vorlesung
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Wintersemester 2009/10 Vorlesung
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Sommersemester 2009 Proseminar


Gäste der Arbeitsgruppe


Publikationen der Nachwuchsgruppe seit 01.07.2016

  1. link R.Mandel, E.Montefusco, B.Pellacci: Oscillating solutions for nonlinear Helmholtz equations. Z. Angew. Math. Phys. 68 (2017), no. 6, Art. 121, 19 pp.
  2. link R.Mandel, D.Scheider: Dual variational methods for a nonlinear Helmholtz system. NoDEA Nonlinear Differential Equations Appl. 25 (2018), no. 2, 25:13.
  3. link R.Mandel: The limiting absorption principle for periodic differential operators and applications to nonlinear Helmholtz equations, Commun. Math. Phys. 368 (2019), no. 2 799-842.
  4. link D.Bonheure, J.-B.Casteras, R.Mandel: On a fourth order nonlinear Helmholtz equation, Journal of the London Mathematical Society 99 (2019), no. 3, 831-852.
  5. link R.Mandel, D.Scheider: Bifurcations of nontrivial solutions of a cubic Helmholtz system, Advances in Nonlinear Analysis, 9(1), 1026–1045.
  6. link R.Mandel: Uncountably many solutions for nonlinear Helmholtz and curl-curl equations with general nonlinearities, Adv. Nonlinear Stud. 19 (2019), no. 3, 569-593.
  7. link J.-B.Casteras, R.Mandel: On Helmholtz equations and counterexamples to Strichartz estimates in hyperbolic space.
  8. link R.Mandel: Dispersive estimates, blow-up and failure of Strichartz estimates for the Schrödinger equation with slowly decaying initial data, Pure And Applied Analysis, vol. 2 (2020), No. 2, 519-532.
  9. link R.Mandel, D.Scheider: An annulus multiplier and applications to the Limiting absorption principle for Helmholtz equations with a step potential, Mathematische Annalen.
  10. link (Preprint) R.Mandel: A uniqueness result for the Sine-Gordon breather.
  11. link D.Scheider: Breather Solutions of the Cubic Klein-Gordon Equation, Nonlinearity.
  12. link (Preprint) R.Mandel, D.Scheider: Variational methods for breather solutions of Nonlinear Wave Equations.
  13. link (Preprint) L.Cossetti, R.Mandel: A limiting absorption principle for Helmholtz systems and time-harmonic isotropic Maxwell's equations.
  14. link (Preprint) A. Fernandez, L. Jeanjean, R.Mandel, M. Maris: Some non-homogeneous Gagliardo-Nirenberg inequalities and application to a biharmonic non-linear Schrödinger equation.
  15. link (Preprint) R.Mandel, D. Scheider, T. Yesil: Dual variational methods for an indefinite nonlinear Helmholtz equation.
  16. link (Preprint) R. Mandel, R. Schippa: Time-harmonic solutions for Maxwell's equations in anisotropic media and Bochner-Riesz estimates with negative index for non-elliptic surfaces.
  17. link (Preprint) R. Mandel, D. Oliveira E Silva: The Tomas-Stein Inequality under the effect of symmetries.
  18. link (Preprint) C. Carvalho, A. D. Kim, L. Lewis, Z. Moitier: Quadrature by parity asymptotic expansions (QPAX) for scattering by high aspect ratio particles.


Publikationen im Projekt B3 des SFB 1173 seit 01.07.2016

  1. link R.Mandel, W.Reichel: A priori bounds and global bifurcations results for frequency combs modeled by the Lugiato-Lefever equation. SIAM J. Appl. Math. 77 (2017), no. 1, 315–345.
  2. link R.Mandel: Global secondary bifurcation, symmetry breaking and period-doubling. Topol. Methods Nonlinear Anal. 53 (2019), no. 2, 779–800.
  3. link J. Gärtner, P. Trocha, R. Mandel, C. Koos, T. Jahnke, W. Reichel: Bandwidth and conversion efficiency analysis of dissipative Kerr soliton frequency combs based on bifurcation theory. Phys. Rev. A 100, 033819.
  4. link J.Gärtner, R.Mandel, W.Reichel: The Lugiato-Lefever equation with nonlinear damping caused by two photon absorption. J Dyn Diff Equat (2021).


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