Titlebook: Qualitative Properties of Dispersive PDEs; Vladimir Georgiev,Alessandro Michelangeli,Raffaele Conference proceedings 2022 The Editor(s) (i

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Allure

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dura-mater

ANIM

A Note on Small Data Soliton Selection for Nonlinear Schrödinger Equations with Potentialdied in (Cuccagna and Maeda, Anal PDE 8(6):1289–1349, 2015; Cuccagna and Maeda, Ann PDE 7:16, 2021). As in (Cuccagna and Maeda, Ann PDE 7:16, 2021), we use the notion of refined profile, but unlike in (Cuccagna and Maeda, Ann PDE 7:16, 2021), we do not modify the modulation coordinates and do not se

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Dynamics of Solutions to the Gross–Pitaevskii Equation Describing Dipolar Bose–Einstein Condensatess. We describe the asymptotic behaviors of solutions for different initial configurations of the initial datum in the energy space, specifically for data below, above, and at the mass–energy threshold. We revisit some properties of powers of the Riesz transforms by means of the decay properties of t

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Nonlinear Schrödinger Equation with Singularitiesgular initial conditions and equations with a delta potential in three dimensions. The existence and uniqueness of solutions are proved in the Colombeau algebra setting and the notion of compatibility of solutions is explored.

Motilin

ARCHE

Heat Equation with Inverse-Square Potential of Bridging Type Across Two Half-Linesem is the lowest energy (zero-momentum) mode of the transmission of the heat flow across a Grushin-type cylinder, a generalisation of an almost-Riemannian structure with compact singularity set. This and related models are reviewed, and the issue is posed of the analysis of the dispersive properties

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