Résumé:
This study is dedicated to investigating the existence of weak solutions for
hyperbolic Kirchhoff-type problems, considering cases both with and without
volume constraints and free boundaries. We employ the hyperbolic discrete
Morse flow, which transforms the original problem into a sequence of mini-
mization problems defined at discrete time intervals. This process ensures the
existence of a minimizer for the discretized functional, which corresponds to
the solution of the discretized problem and subsequently provides a weak so-
lution to the original problem. The non-local terms arising from the Kirchhoff
component, volume constraint, and free boundary condition present significant
challenges that require innovative methods to tackle. These complexities are
a key focus of our research. Furthermore, we present numerical simulations to
better illustrate our results’ physical implications.
