Este seminario está dedicado a la exposición de avances recientes en el área de ecuaciones diferenciales no lineales. Participan en él expertos internacionales y nacionales, becarios posdoctorales y estudiantes de doctorado.
Responsables: Dra. Mónica Clapp, Dr.Alberto Saldaña y Dr. Víctor Hernández
26 de Abril de 2025
10:00 hrs
A weighted anisotropic spectral optimization problem arising in population dynamics
Delia Schiera
Universidade de Lisboa
I will discuss a weighted eigenvalue problem with anisotropic diffusion in bounded Lipschitz domains under Robin boundary conditions.We prove the existence of two positive eigenvalues λpm respectively associated with a positive and a negative eigenfunction, and we analyze the minimization of λpm with respect to the sign-changing weight. This problem naturally arises in the study of the optimal spatial arrangement of resources for a species to survive in a heterogeneous habitat. The optimal weights are of bang-bang type, namely piece-wise constant functions that take only two values. We completely solve the optimization problem in one dimension, in the case of homogeneous Dirichlet or Neumann conditions, showing new phenomena induced by the presence of the anisotropic diffusion.