Juan Alberto Molina García
Independent researcher, Spain
Publications
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Research Article
Partial Differential Equations and Inverse Problems in Non-Separable Banach Spaces
Author(s): Juan Alberto Molina García*
The classical functional–analytic theory of partial differential equations (PDEs) is predominantly developed within separable Banach and Hilbert spaces, where compactness, countable bases, and metrisation techniques play a central methodological role. However, a growing number of mathematical models arising in infinite-dimensional dynamics, continuum mechanics, control theory, inverse problems, and data-driven systems naturally lead to non-separable functional settings. This article develops a systematic framework for the analysis of partial differential equations and inverse problems in NSBS, extending existence, uniqueness, and stability results beyond the separable paradigm. We introduce a functional-analytic formulation of PDEs on NSBS that avoids reliance on compact embeddings or countable approximations, replacing them with weak, weak* and approximate compactness.. Read More»