Theoretical results and numerical simulations for the null controllability of a nonlinear parabolic system with a multiplicative control in moving domains
摘要
In this article, we discuss the local and global null controllability of a coupled nonlinear parabolic system in a domain with a time-evolving boundary due to the influence of a control force with a multiplicative component acting in a predefined subregion. Our approach is based on the application of Liusternik’s inverse mapping theorem, which requires the validation of an appropriate Carleman estimate. In addition to the theoretical developments presented, we introduce an iterative quasi-Newton algorithm designed to guide numerical simulations and provide guidelines for the interpretation of theoretical results.