Qualitative analysis for a new constrained hyperbolic p-Kirchhoff type problem involving free boundary

In this work, we investigate the existence of weak solutions for a constrained hyperbolic p-Kirchhoff type problem involving a free boundary. We employ the Discrete Morse Flow (DMF) approach, which reformulates the original problem as a sequence of minimization problems in discrete time intervals. This ensures the existence of a minimizer for the discretized functional, which in turn serves as a weak solution to the main problem. The presence of non-local terms, introduced by the p-Kirchhoff term and the volume constraint with a free boundary, poses significant analytical challenges. Our study provides a rigorous treatment to overcome these difficulties. Furthermore, we present numerical simulations to illustrate the physical implications of our results.