EXISTENCE AND UNIQUENESS OF A WEAK SOLUTION OF AN EXTENSIBLE BEAM ON A MOVING DOMAIN

EXISTENCE AND UNIQUENESS OF A WEAK SOLUTION OF AN EXTENSIBLE BEAM ON A MOVING DOMAIN

Various methods exist to address the challenges posed by moving domain problems, including the transform method, penalty method, and push-forward and pull-back method. These methods play a crucial role in transforming non-cylindrical domain problems into cylindrical domain problems. In [15], the existence of at least one weak solution for a more general extensible beam was established. However, this paper does not specifically address the uniqueness of solutions and explore their relationship within any finite-dimensional space. Our primary objective is to formulate approximate solutions in a finite-dimensional space using the penalty method, with a focus on achieving uniqueness. Furthermore, we present an illustrative example to enhance the understanding of the concepts discussed.