3 papers
math.AP2026
Homogenization of Dynamic Signorini-Type Problems on Critically Oscillating Boundaries under Time-Periodic Forcing
J. I. Diaz, A. V. Podolskyi, T. A. Shaposhnikova
We study the homogenization, in the critical scaling regime, of a boundary value problem with a nonlinear dynamic Signorini-type condition posed on a rapidly oscillating portion of…
math.AP2025
New cost terms through the homogenization of an optimal control problem under dynamic boundary conditions on the microscopic particles
J. I. DÃaz, T. A. Shaposhnikova, A. V. Podolskiy
Given an optimal control problem on a heterogeneous body with a periodical structure of particles depending on a small parameter e, we study the asymptotic behavior, as e converges…
math.AP2024
New unexpected limit operators for homogenizing optimal control parabolic problems with dynamic reaction flow on the boundary of critically scaled particles
Jesus Ildefonso Diaz, Alexander V. Podolskiy, Tatiana A. Shaposhnikova
We pass to the limit in the homogenization of an optimal control problem associated with a parabolic equation with a dynamic boundary condition. New unexpected terms appear due to…