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Pré-Publication, Document De Travail Année : 2023

The Porous Media Schrödinger Equation : Feynman-type Motivation, Well-Posedness and Control Interpretation

Résumé

This paper's aim is threefold. First, using Feynman's path approach to the derivation of the classical Schrödinger's equation in [7] and by introducing a slight path (or wave) dependency of the action, we derive a new class of equations of Schrödinger type where the driving operator is no longer the Laplace one but rather of complex porous media-type. Second, using suitable concepts of monotonicity in the complex setting and on appropriate functional spaces, we show the existence and uniqueness of the equation we have previously introduced. Finally, using Fitzpatrick's characterization of maximal monotone operators (cf. [8]), we propose a Brézis-Ekeland type characterization of the solution via a control problem.
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Dates et versions

hal-04220614 , version 1 (28-09-2023)

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Ioana Ciotir, Dan Goreac, Juan Li, Xinru Zhang. The Porous Media Schrödinger Equation : Feynman-type Motivation, Well-Posedness and Control Interpretation. 2023. ⟨hal-04220614⟩
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