Semi-algebraic sets method in PDE and mathematical physics

This paper surveys recent progress in the analysis of nonlinear partial differential equations using Anderson localization and semi-algebraic sets method. We discuss the application of these tools from linear analysis to nonlinear equations such as the nonlinear Schrödinger equations, the nonlinear...

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Bibliographic Details
Published in:Journal of mathematical physics 2021-02, Vol.62 (2)
Main Author: Wang, W.-M.
Format: Article
Language:English
Subjects:
Algebra
Anderson localization
Linear analysis
Mathematical analysis
Nonlinear analysis
Nonlinear differential equations
Nonlinear equations
Partial differential equations
Physics
Schrodinger equation
Wave equations
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Summary:This paper surveys recent progress in the analysis of nonlinear partial differential equations using Anderson localization and semi-algebraic sets method. We discuss the application of these tools from linear analysis to nonlinear equations such as the nonlinear Schrödinger equations, the nonlinear Klein–Gordon equations (nonlinear wave equations), and the nonlinear random Schrödinger equations on the lattice. We also review the related linear time-dependent problems.
ISSN:0022-2488
1089-7658
DOI:10.1063/5.0031622