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math.AP2025
Inverse Random Source and Cauchy Problems for Semi-Discrete Stochastic Parabolic Equations in Arbitrary Dimensions
Rodrigo Lecaros, Ariel A. Pérez, Manuel F. Prado
In this paper, we study two types of inverse problems for space semi-discrete stochastic parabolic equations in arbitrary dimensions. The first problem concerns a semi-discrete inv…
math.AP2025
Lipschitz stability and reconstruction in inverse problems for semi-discrete parabolic operators
Rodrigo Lecaros, Juan López-Ríos, Ariel A. Pérez
This work addresses an inverse problem for a semi-discrete parabolic equation, consisting of identifying the right-hand side of the equation from solution measurements at an interm…
math.OC2025
Carleman estimate for semi-discrete stochastic parabolic operators in arbitrary dimension and applications to controllability
Rodrigo Lecaros, Ariel A. Pérez, Manuel F. Prado
This paper considers a semi-discrete forward stochastic parabolic operator with homogeneous Dirichlet conditions in arbitrary dimensions. We show the lack of null controllability f…