Partial differential equations, Mathematical physics
Nonlinear Helmholtz equations with sign-changing diffusion coefficient
Comptes Rendus. Mathématique, Volume 360 (2022) no. G5, pp. 513-538.

In this paper, we study nonlinear Helmholtz equations with sign-changing diffusion coefficients on bounded domains. The existence of an orthonormal basis of eigenfunctions is established making use of weak T-coercivity theory. All eigenvalues are proved to be bifurcation points and the bifurcating branches are investigated both theoretically and numerically. In a one-dimensional model example we obtain the existence of infinitely many bifurcating branches that are mutually disjoint, unbounded, and consist of solutions with a fixed nodal pattern.

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DOI: 10.5802/crmath.322
Classification: 35B32, 47A10
Mandel, Rainer 1; Moitier, Zoïs 1; Verfürth, Barbara 2

1 Karlsruhe Institute of Technology, Institute for Analysis, Englerstraße 2, D-76131 Karlsruhe, Germany.
2 Karlsruhe Institute of Technology, Institute for Applied and Numerical Mathematics Englerstraße 2, D-76131 Karlsruhe, Germany.
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Mandel, Rainer; Moitier, Zoïs; Verfürth, Barbara. Nonlinear Helmholtz equations with sign-changing diffusion coefficient. Comptes Rendus. Mathématique, Volume 360 (2022) no. G5, pp. 513-538. doi : 10.5802/crmath.322. http://www.numdam.org/articles/10.5802/crmath.322/

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