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Differentiaalvergelijkingen (Elliptische). --- Differentiaalvergelijkingen (Parabolische). --- Inégalités variationnelles [Mathématiques]. --- Equations différentielles élliptiques. --- Equations différentielles paraboliques. --- Variatieongelijkheden [Wiskunde].

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These lecture notes are woven around the subject of Burgers' turbulence/KPZ model of interface growth, a study of the nonlinear parabolic equation with random initial data. The analysis is conducted mostly in the space-time domain, with less attention paid to the frequency-domain picture. However, the bibliography contains a more complete information about other directions in the field which over the last decade enjoyed a vigorous expansion. The notes are addressed to a diverse audience, including mathematicians, statisticians, physicists, fluid dynamicists and engineers, and contain both rigorous and heuristic arguments. Because of the multidisciplinary audience, the notes also include a concise exposition of some classical topics in probability theory, such as Brownian motion, Wiener polynomial chaos, etc.

Partial differential equations --- Interfaces (Physical sciences) --- Turbulence --- Burgers equation --- Differential equations, Parabolic --- Mathematical models --- Mathematical Theory --- Atomic Physics --- Physics --- Mathematics --- Physical Sciences & Mathematics --- Differentiaalvergelijkingen [Parabolische ] --- Differential equations [Parabolic] --- Diffusion equation [Nonlinear ] --- Equations differentielles paraboliques --- Heat flow equation [Nonlinear ] --- Interface (Physical sciences) --- Partial differential equations. --- Probabilities. --- Partial Differential Equations. --- Probability Theory and Stochastic Processes. --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Burgers equation. --- Mathematical models. --- Diffusion equation, Nonlinear --- Heat flow equation, Nonlinear --- Nonlinear diffusion equation --- Nonlinear heat flow equation --- Heat equation --- Navier-Stokes equations --- Interfaces (Physical sciences) - Mathematical models --- Turbulence - Mathematical models

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Bedieningstheorie --- Commande [Theorie de la ] --- Control theory --- Differentiaalvergelijkingen [Niet-lineaire ] --- Differentiaalvergelijkingen [Parabolische ] --- Differential equations [Nonlinear ] --- Differential equations [Parabolic] --- Equations differentielles paraboliques --- Equations différentielles non-linéaires --- Mathematical optimization --- Optimalisation mathématique --- Wiskundige optimisatie --- Differential equations, Parabolic --- Differential equations, Nonlinear --- 519.6 --- 681.3 *G18 --- 681.3*J7 --- Nonlinear differential equations --- Nonlinear theories --- Parabolic differential equations --- Parabolic partial differential equations --- Differential equations, Partial --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Dynamics --- Machine theory --- Computational mathematics. Numerical analysis. Computer programming --- Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- Computers in other systems: command and control; consumer products; industrial control; process control; publishing; real time--See also {681.3*C3} --- Control theory. --- Mathematical optimization. --- Differential equations, Parabolic. --- Differential equations, Nonlinear. --- 681.3*J7 Computers in other systems: command and control; consumer products; industrial control; process control; publishing; real time--See also {681.3*C3} --- 681.3 *G18 Partial differential equations: difference methods; elliptic equations; finite element methods; hyperbolic equations; method of lines; parabolic equations (Numerical analysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming