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Normal forms (Mathematics) --- Perturbation (Mathematics) --- Wave equation --- Numerical solutions.

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This volume presents an accessible overview of mathematical control theory and analysis of PDEs, providing young researchers a snapshot of these active and rapidly developing areas. The chapters are based on two mini-courses and additional talks given at the spring school "Trends in PDEs and Related Fields" held at the University of Sidi Bel Abbès, Algeria from 8-10 April 2019. In addition to providing an in-depth summary of these two areas, chapters also highlight breakthroughs on more specific topics such as: Sobolev spaces and elliptic boundary value problems Local energy solutions of the nonlinear wave equation Geometric control of eigenfunctions of Schrödinger operators Research in PDEs and Related Fields will be a valuable resource to graduate students and more junior members of the research community interested in control theory and analysis of PDEs.

Differential equations --- differentiaalvergelijkingen --- systeemtheorie --- Control theory. --- Differential equations, Partial. --- Differential equations, Partial --- Teoria de control --- Equacions en derivades parcials --- Solucions numèriques --- Numerical solutions.

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Maxwell equations --- Finite element method. --- Maxwell equations. --- Numerical solutions. --- Equations, Maxwell --- Differential equations, Partial --- Electromagnetic theory --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Numerical analysis --- Isogeometric analysis --- Equacions de Maxwell

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Differential equations, Partial --- Numerical solutions. --- Numerical solutions --- Data processing. --- Partial differential equations --- Numerical analysis --- Equacions en derivades parcials --- Solucions numèriques --- Anàlisi numèrica --- EDPs --- Equació diferencial en derivades parcials --- Equacions diferencials en derivades parcials --- Equacions diferencials parcials --- Equacions diferencials --- Dispersió (Matemàtica) --- Equació d'ona --- Equació de Dirac --- Equació de Fokker-Planck --- Equació de Schrödinger --- Equacions de Navier-Stokes --- Equacions de Hamilton-Jacobi --- Equacions de Maxwell --- Equacions de Monge-Ampère --- Equacions de Von Kármán --- Equacions diferencials el·líptiques --- Equacions diferencials hiperbòliques --- Equacions diferencials parabòliques --- Equacions diferencials parcials estocàstiques --- Funcions harmòniques --- Laplacià --- Problema de Cauchy --- Problema de Neumann --- Teoria espectral (Matemàtica)

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Anàlisi numèrica --- Numerical grid generation (Numerical analysis) --- Mètodes numèrics --- Algorismes --- Anàlisi matemàtica --- Teoria de l'aproximació --- Anàlisi d'error (Matemàtica) --- Anàlisi d'intervals (Matemàtica) --- Càlculs numèrics --- Equacions diferencials estocàstiques --- Integració numèrica --- Interpolació (Matemàtica) --- Mètodes de Galerkin --- Mètode de Montecarlo --- Mètode dels elements finits --- Mètodes iteratius (Matemàtica) --- Nomografia (Matemàtica) --- Rutes aleatòries (Matemàtica) --- Solucions numèriques --- Coordinate generation, Numerical (Numerical analysis) --- Generation of numerical grids (Numerical analysis) --- Grid generation, Numerical (Numerical analysis) --- Mesh generation, Numerical (Numerical analysis) --- Numerical coordinate generation (Numerical analysis) --- Numerical mesh generation (Numerical analysis) --- Boundary value problems --- Differential equations, Partial --- Nets (Mathematics) --- Numerical analysis --- Numerical solutions