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Communication Dans Un Congrès Année : 2022

Nonlinear Helmholtz equations with sign-changing diffusion coefficient

Résumé

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. We also extend the numerics to a Drude model.
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Dates et versions

hal-03830606 , version 1 (26-10-2022)

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  • HAL Id : hal-03830606 , version 1

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Rainer Mandel, Zoïs Moitier, Barbara Verfürth. Nonlinear Helmholtz equations with sign-changing diffusion coefficient. 15th International Conference on Mathematical and Numerical Aspects of Wave Propagation (WAVES 2022), Jul 2022, Palaiseau, France. ⟨hal-03830606⟩

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