Banca de DEFESA: MARISA DA CUNHA BEZERRA

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : MARISA DA CUNHA BEZERRA
DATE: 24/11/2025
TIME: 10:00
LOCAL: Unidade Acadêmica de Matemática
TITLE:

Exact Boundary Controllability for the Wave Equation in a Non-Cylindrical Domain

KEY WORDS:

Wave equation, Non-cylindrical domain, Exact controllability.

PAGES: 132
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUBÁREA: Análise
SPECIALTY: Equações Diferenciais Parciais
SUMMARY:

In this work, we investigate the problem of exact controllability for the equation
$$u''-\Delta u=0 \quad \text{in} \quad \widehat{Q},$$
where $\hat{Q}$ is a non-cylindrical domain of $\mathbb{R}^{n+1}$. To overcome the challenges imposed by the non-cylindrical geometry, we perform an appropriate change of variables, which allows us to transform problem \eqref{Eq.Onda_} into an equivalent problem in a cylindrical domain. Thus, we study the exact controllability of the equation
$$w'' - \displaystyle\sum_{i,j=1}^n \frac{\partial}{\partial x_i} \left( a_{ij}(x,t) \frac{\partial w}{\partial x_j} \right) + \sum_{i=1}^n b_i(x,t) \frac{\partial w'}{\partial x_i} + \sum_{i=1}^n \beta_i(x,t) \frac{\partial w}{\partial x_i} = 0 \quad \text{in} \quad Q,$$
where $Q=\Omega \times (0,T)$ is a cylinder, with $\Omega \subset \mathbb{R}^n$ a bounded domain. The well-posedness results are established via the Galerkin method, ensuring existence and uniqueness of solutions. In this setting, we study the exact controllability using the Hilbert Uniqueness Method (HUM) and, finally, demonstrate the equivalence between these systems, which ensures that the controllability results obtained in the cylinder extend rigorously to the non-cylindrical domain $\hat{Q}.$

 

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