Exact controllability to trajectory and approximate controllability for semilinear heat equation

Author(s)

Pedro Álvares Muiños

• Document type: Master's Dissertation
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
• Defense date: 2023-09-22

Examining board members

Bianca Morelli Rodolfo Calsavara; Maurício Cardoso Santos; João Vitor da Silva

• Advisor: Bianca Morelli Rodolfo Calsavara

Abstract

This thesis aims to study a controllability property of a partial differential equation (PDE). In general, a controllability problem for PDE consists in acting on the solutions of the PDE (trajectories) through a control (that might be the boundary condition or the nonhomogeneous term of the equation). More specifically, for some final time and some initial value, a control is sought such that the trajectory of the initial value problem with initial data satisfies some desired condition for the final time. Throughout this work it was studied an initial and boundary value problem for the semilinear heat equation where the control was applied on the the nonhomogeneous term of the equation. Results regarding the exact and approximate controllability of this system were obtained. Their proofs consisted in seeking enough conditions with respect to the system, particularly to the nonlinear term of the equation, such that it satisfies or not the property of exact/approximate controllability (AU)

• FAPESP's process: 21/00196-9 - Exact controllability to trajectories and approximate controllability for semilinear heat equation
• Grantee: Pedro Álvares Muiños
• Support Opportunities: Scholarships in Brazil - Master