Nonlinear Helmholtz equations with sign-changing diffusion coefficient
Analysis of PDEs
2021-12-22 v4
Abstract
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.
Cite
@article{arxiv.2107.14516,
title = {Nonlinear Helmholtz equations with sign-changing diffusion coefficient},
author = {Rainer Mandel and Zoïs Moitier and Barbara Verfürth},
journal= {arXiv preprint arXiv:2107.14516},
year = {2021}
}