By MSc. Paula Castro, estudiante del Programa de Doctorado en Matemática Aplicada EPN, Ecuador
Seminar Date: 2021-10-07
In this talk, we present a rigorous analysis for the 4D?VAR data assimilation problem in its infinite-dimensional setting. We use maximal parabolic regularity tools jointly with real and complex interpolation theory to fulfill the requirements of the problem, such as having an initial condition belonging to a not so regular space, such as $L^{\beta}(\Omega)$, with $\beta>2$ ($n=2$) or $3<\beta<6$ ($n=3$) instead of the space $H_0^1(\Omega)$. Due to the nature of our problem, pointwise observations appear in the cost function. Therefore, we must guarantee continuity in the spatial variable for the solution space, possibly through embedding results.