Direct and Inverse Problems with Applications
Springer International Publishing (Verlag)
978-3-031-98644-4 (ISBN)
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This volume presents the extended abstracts from the 2024 Summer School organized by the Ghent Analysis and PDE Center. The school focused on equipping participants with a broad spectrum of mathematical tools for addressing both direct and inverse problems across various fields. Through a combination of lectures, problem-solving sessions, and collaborative discussions, the program fostered the development of innovative methods and techniques. The lectures also include broader related topics in mathematical analysis and partial differential equations, offering a comprehensive perspective on current research directions in the field.
Mariana Chatzakou is a postdoctoral researcher at Ghent University, Belgium.
Michael Ruzhansky is a senior full professor of Mathematics at Ghent University in Belgium, and a professor of Mathematics at Queen Mary University of London in the United Kingdom.
Karel Van Bockstal is a postdoctoral researcher at Ghent University, Belgium.
Fourier algebras and homomorphisms.- Dispersion phenomena and applications to evolution equations.- Subriemannian geometry and analysis of hypoelliptic PDE.- Stability results for Sobolev, logarithmic Sobolev, and related inequalities.- Semiconcavity, viscosity solutions and the square distance in Carnot groups.- Direct and inverse nonstationary scattering problems for Dirac-type system.- Quantitative homogenisation for differential equations with highly anisotropic partially degenerating coefficients.- Rigidity results for evolution PDEs on homogeneuos Lie groups.- An overview of dualities in non-commutative harmonic analysis.- Colombeau type extensions, assymptotic scales.- Analytical solutions to the Laplace equation on a hemispherical domain.- Uniform spectral asymptotics for high-contrast periodic media.- Asymptotic mean value formulas for the -Laplacian in the Euclidean space and in the Heisenberg Group.- Global solutions for a class of nonlinear evolution equations in supercritical spaces.- An index transform method for solutions of the boundary value problems in a wedge.
| Erscheinungsdatum | 20.07.2025 |
|---|---|
| Reihe/Serie | Research Perspectives Ghent Analysis and PDE Center | Trends in Mathematics |
| Zusatzinfo | VIII, 235 p. 8 illus., 7 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Schlagworte | Applications of PDEs • Direct and inverse problems • functional inequalities • Mathematical Analysis • PDEs |
| ISBN-10 | 3-031-98644-X / 303198644X |
| ISBN-13 | 978-3-031-98644-4 / 9783031986444 |
| Zustand | Neuware |
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