Titre : Zoïs Moitier (Karlsruhe Institute of Technology, département de Mathématiques). Nonlinear Helmholtz equations with sign-changing diffusion coefficient.
Contact : Jean-François Fritsch  
Date : 18/11/2021
Lieu : 14h30, amphi 2234

In this talk, we study nonlinear Helmholtz equations with sign-changing diffusion coefficients on bounded domains of the form - div(σ(x)∇u ) - λc(x)u =  g(x,u)  . Using weak T -coercivity theory, we can establish the existence of an orthonormal basis of eigenfunctions of the linear part
-c(x)-1div(σ(x)u). Then, all eigenvalues are proved to be bifurcation points and we investigate the bifurcating branches both theoretically and numerically. As a fundamental example, we look at some one-dimensional model, we obtain the existence of infinitely many bifurcating branches that are mutually disjoint, unbounded, and consist of solutions with a fixed nodal pattern.