scholarly journals Scattering of the focusing energy-critical NLS with inverse square potential in the radial case

2021 ◽  
Vol 20 (1) ◽  
pp. 77-99
Author(s):  
Kai Yang ◽  
Keyword(s):  
Radial Case

Erdélyi–Kober fractional integrals and radon transforms for mutually orthogonal affine planes

2020 ◽  
Vol 23 (4) ◽  
pp. 967-979
Author(s):  
Boris Rubin ◽  
Yingzhan Wang
Keyword(s):  
Fractional Integrals ◽  
Radon Transforms ◽  
Affine Planes ◽  
Inversion Formulas ◽  
Radial Functions ◽  
Compactly Supported ◽  
Radial Case ◽  
Compactly Supported Functions

AbstractWe apply Erdélyi–Kober fractional integrals to the study of Radon type transforms that take functions on the Grassmannian of j-dimensional affine planes in ℝn to functions on a similar manifold of k-dimensional planes by integration over the set of all j-planes that meet a given k-plane at a right angle. We obtain explicit inversion formulas for these transforms in the class of radial functions under minimal assumptions for all admissible dimensions. The general (not necessarily radial) case, but for j + k = n − 1, n odd, was studied by S. Helgason [8] and F. Gonzalez [4, 5] on smooth compactly supported functions.

Blow-up of solutions to cubic nonlinear Schrödinger equations with defect: The radial case

2017 ◽  
Vol 6 (2) ◽  
pp. 183-197 ◽  
Author(s):  
Olivier Goubet ◽  
Emna Hamraoui
Keyword(s):  
Blow Up ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Radial Solutions ◽  
Nls Equation ◽  
Nonlinear Schrödinger ◽  
Radial Case ◽  
Nonlinear Schrodinger Equations ◽  
Dimension 2

AbstractIn this article we investigate both numerically and theoretically the influence of a defect on the blow-up of radial solutions to a cubic NLS equation in dimension 2.

scholarly journals Resolution analysis of tomographic slug test head data: Two‐dimensional radial case

2015 ◽  
Vol 51 (4) ◽  
pp. 2356-2376 ◽  
Author(s):  
Daniel Paradis ◽  
Erwan Gloaguen ◽  
René Lefebvre ◽  
Bernard Giroux
Keyword(s):  
Two Dimensional ◽  
Slug Test ◽  
Radial Case ◽  
Resolution Analysis

scholarly journals Nonlinear heat equation: the radial case

1999 ◽  
Vol 5 (4) ◽  
pp. 849-870
Author(s):  
Arthur Ramiandrisoa ◽  
Keyword(s):  
Heat Equation ◽  
Nonlinear Heat Equation ◽  
Radial Case
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