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math.AP2026
Small-time local control of a Schrödinger equation: a negative and a positive quadratic result
Karine Beauchard, Frédéric Marbach, Thomas Perrin
We study the small-time local controllability (STLC) of a bilinear Schrödinger equation with Neumann boundary conditions near its ground state. We focus on the degenerate case whe…
math.AP2025
Nonlinear Forward-Backward Problems
Anne-Laure Dalibard, Frédéric Marbach, Jean Rax
We prove the existence and uniqueness of strong solutions to the equation in the vicinity of the linear shear flow, subject to perturbations of the source term…
math.AP2025
Linear and nonlinear parabolic forward-backward problems
Anne-Laure Dalibard, Frédéric Marbach, Jean Rax
The purpose of this paper is to investigate the well-posedness of several linear and nonlinear equations with a parabolic forward-backward structure, and to highlight the similarit…