Fakultät für Mathematik
Webrelaunch 2020
Fakultät für Mathematik
Startseite
Institute
Institut für Analysis
Ehemalige Nachwuchsgruppen
Nachwuchsgruppe Nichtlineare Helmholtzgleichungen

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.

Leitung: PD Dr. Rainer Mandel

Personen in der Nachwuchsgruppe Nichtlineare Helmholtzgleichungen
Name Tel. E-Mail

Aktuelles Lehrangebot
Semester Titel Typ
Wintersemester 2022/23 Verzweigungstheorie Vorlesung
Wintersemester 2020/21 Seminar (Nichtlineare Funktionalanalysis) Seminar
Sommersemester 2020 Nichtlineare Funktionalanalysis Vorlesung
Wintersemester 2018/19 Seminar Seminar
Sommersemester 2018 Boundary and Eigenvalue Problems Vorlesung
Wintersemester 2017/18 Variational and Topological Methods in Bifurcation Theory Vorlesung
Seminar Bifurcation Theory Seminar
Sommersemester 2017 Verzweigungstheorie Vorlesung
Wintersemester 2013/14 Analysis III Vorlesung
Proseminar (Ungleichungen) Proseminar
Sommersemester 2013 Analysis II Vorlesung
Proseminar ( Analysis) Proseminar
Wintersemester 2012/13 Analysis I Vorlesung
Sommersemester 2012 Numerische Methoden (Elektrotechnik, Meteorologie, Geodäsie, Geoinformatik) Vorlesung
Höhere Mathematik II (Analysis) für die Fachrichtung Informatik Vorlesung
Wintersemester 2011/12 Höhere Mathematik I (Analysis) für die Fachrichtung Informatik Vorlesung
Sommersemester 2011 Seminar (Differentialgleichungen der Mathematischen Physik) Seminar
Wintersemester 2010/11 Nichtlineare Randwertprobleme/Nonlinear boundary value problems Vorlesung
Seminar (Randwertprobleme/boundary value problems) Seminar
Sommersemester 2010 Boundary and Eigenvalue Problems Vorlesung
Seminar Partial Differential Equations Seminar
Wintersemester 2009/10 Partielle Differentialgleichungen / Partial Differential Equations Vorlesung
Proseminar(Ungleichungen) Proseminar
Numerische Mathematik für die Fachrichtung Elektroingenieurwesen Vorlesung
Sommersemester 2009 Proseminar (Analysis: Zahlen) Proseminar


Gäste der Arbeitsgruppe


Aktuelle Preprints der Nachwuchsgruppe

  1. link R. Mandel, D. Oliveira E Silva: The Tomas-Stein Inequality under the effect of symmetries.
  2. link R. Mandel: On Gagliardo-Nirenberg Inequalities with vanishing symbols.
  3. link R. Mandel: A simple variational approach to Nonlinear Maxwell equations.
  4. link C. Carvalho, Z. Moitier: Scattering resonances in unbounded transmission problems with sign-changing coefficient.

Publikationen der Nachwuchsgruppe

  1. link R. Mandel, Z. Moitier, B. Verfürth: Nonlinear Helmholtz equations with sign-changing diffusion coefficient. C. R. Math. Acad. Sci. Paris 360 (2022), 513–538.
  2. link R. Griesmaier, M. Knöller, R. Mandel: Inverse medium scattering for a nonlinear Helmholtz equation. J. Math. Anal. Appl. 515 (2022), no. 1, Paper No. 126356, 27 pp.
  3. link A. Fernandez, L. Jeanjean, R.Mandel, M. Maris: Non-homogeneous Gagliardo-Nirenberg inequalities in RN and application to a biharmonic non-linear Schrödinger equation. J. Differential Equations 330 (2022), 1–65.
  4. link 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. Ann. Henri Poincaré 23 (2022), no. 5, 1831–1882.
  5. link C. Carvalho, A. D. Kim, L. Lewis, Z. Moitier: Quadrature by parity asymptotic expansions (QPAX) for scattering by high aspect ratio particles. Multiscale Model. Simul. 19 (2021), no. 4, 1857–1884.
  6. link R. Mandel: Ground states for Maxwell's equations in nonlocal nonlinear media. Partial Differ. Equ. Appl. 3 (2022), no. 2, Paper No. 22, 16 pp.
  7. link R. Mandel: A uniqueness result for the Sine-Gordon breather. Partial Differ. Equ. Appl. 2 (2021), no. 2, Paper No. 26, 8 pp.
  8. link L. Cossetti, R. Mandel: A limiting absorption principle for Helmholtz systems and time-harmonic isotropic Maxwell's equations. J. Funct. Anal. 281 (2021), no. 11, Paper No. 109233, 41 pp.
  9. link R. Mandel, D. Scheider: Variational methods for breather solutions of nonlinear wave equations. Nonlinearity 34 (2021), no. 6, 3618–3640.
  10. link R. Mandel, D. Scheider, T. Yesil: Dual variational methods for a nonlinear Helmholtz equation with sign-changing nonlinearity. Calc. Var. Partial Differential Equations 60 (2021), no. 4, Paper No. 133, 13 pp.
  11. link D. Scheider: Breather solutions of the cubic Klein-Gordon equation. Nonlinearity 33 (2020), no. 12, 7140–7166.
  12. link J.-B. Casteras, R. Mandel: On Helmholtz equations and counterexamples to Strichartz estimates in hyperbolic space. Int. Math. Res. Not. IMRN 2021, no. 7, 4838–4863.
  13. link R. Mandel, D. Scheider: An annulus multiplier and applications to the Limiting absorption principle for Helmholtz equations with a step potential. Math. Ann. 379 (2021), no. 1-2, 865–907.
  14. 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.
  15. link R. Mandel, D. Scheider: Bifurcations of nontrivial solutions of a cubic Helmholtz system. Advances in Nonlinear Analysis, 9(1), 1026–1045.
  16. 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.
  17. 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.
  18. 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.
  19. link R. Mandel, D. Scheider: Dual variational methods for a nonlinear Helmholtz system. NoDEA Nonlinear Differential Equations Appl. 25 (2018), no. 2, 25:13.
  20. 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.


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. Dynam. Differential Equations 34 (2022), no. 3, 2201–2227.


Weitere Forschungsaktivitäten