Author:
Bentata Fatima Ezahra,Mokhtari Abdelhak,Boumaza Nouri
Abstract
In this study, we explore the existence of weak solutions for a hyperbolic Kirchhoff-type problem constrained by volume with a free boundary. Our approach leverages the hyperbolic discrete Morse flow. The presence of both a non-local term and a free boundary in our problem introduces significant challenges, necessitating unconventional methods for resolution. These unique difficulties are at the heart of our investigation. Specifically, the non-local term complicates the application of traditional analytical techniques, while the free boundary condition requires careful handling to ensure the existence of solutions. Our methodology involves a detailed examination of the hyperbolic discrete Morse flow framework, adapting it to address the intricacies introduced by the non-local term and the free boundary. Through rigorous mathematical analysis and the development of novel techniques, we aim to establish the conditions under which weak solutions exist.
Publisher
South Florida Publishing LLC
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