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.
Semi-algebraic sets method in PDE and mathematical physics
Note: This paper is part of the Special Issue on Celebrating the work of Jean Bourgain.
W.-M. Wang; Semi-algebraic sets method in PDE and mathematical physics. J. Math. Phys. 1 February 2021; 62 (2): 021506. https://doi.org/10.1063/5.0031622
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