Seminar
Title : | 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 |
Place : | 14h30, amphi 2234 |
In this talk, we study nonlinear Helmholtz equations with sign-changing diffusion
coefficients on bounded domains of the form .
Using weak -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.