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Averaging method (Differential equations) --- Differential equations --- Adiabatic invariants --- Asymptotic theory --- Differential equations - Asymptotic theory --- ADIABATIC INVARIANTS --- AVERAGING METHOD (DIFFERENTIAL EQUATIONS) --- DIFFERENTIAL EQUATIONS --- ASYMPTOTIC THEORY

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Thermodynamically constrained averaging theory provides a consistent method for upscaling conservation and thermodynamic equations for application in the study of porous medium systems.  The method provides dynamic equations for phases, interfaces, and common curves that are closely based on insights from the entropy inequality. All larger scale variables in the equations are explicitly defined in terms of their microscale precursors, facilitating the determination of important parameters and macroscale state equations based on microscale experimental and computational analysis. The method requires that all assumptions that lead to a particular equation form be explicitly indicated, a restriction which is useful in ascertaining the range of applicability of a model as well as potential sources of error and opportunities to improve the analysis.

Averaging method (Differential equations). --- Differential equations, Linear. --- Porous. --- Porous materials --- Thermodynamics --- Chemical & Materials Engineering --- Engineering & Applied Sciences --- Materials Science --- Mathematical models --- Mathematics --- Porous materials. --- Porous media --- Earth sciences. --- Geology --- Mineralogy. --- Geophysics. --- Thermodynamics. --- Earth Sciences. --- Geophysics/Geodesy. --- Quantitative Geology. --- Statistical methods. --- Materials --- Porosity --- Physical geography. --- GeologyxMathematics. --- Chemistry, Physical and theoretical --- Dynamics --- Mechanics --- Physics --- Heat --- Heat-engines --- Quantum theory --- Physical geology --- Crystallography --- Minerals --- Geography --- Geology—Statistical methods. --- Geological physics --- Terrestrial physics --- Earth sciences

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Perturbation theory and in particular normal form theory has shown strong growth during the last decades. So it is not surprising that the authors have presented an extensive revision of the first edition of the Averaging Methods in Nonlinear Dynamical Systems book. There are many changes, corrections and updates in chapters on Basic Material and Asymptotics, Averaging, and Attraction. Chapters on Periodic Averaging and Hyperbolicity, Classical (first level) Normal Form Theory, Nilpotent (classical) Normal Form, and Higher Level Normal Form Theory are entirely new and represent new insights in averaging, in particular its relation with dynamical systems and the theory of normal forms. Also new are surveys on invariant manifolds in Appendix C and averaging for PDEs in Appendix E. Since the first edition, the book has expanded in length and the third author, James Murdock has been added. Review of First Edition "One of the most striking features of the book is the nice collection of examples, which range from the very simple to some that are elaborate, realistic, and of considerable practical importance. Most of them are presented in careful detail and are illustrated with profuse, illuminating diagrams." - Mathematical Reviews.

Differential equations, Nonlinear --- Differentiable dynamical systems. --- Averaging method (Differential equations) --- Numerical solutions. --- Method of averaging (Differential equations) --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Numerical analysis --- Numerical solutions --- Differential equations, partial. --- Global analysis (Mathematics). --- Dynamical Systems and Ergodic Theory. --- Partial Differential Equations. --- Theoretical, Mathematical and Computational Physics. --- Analysis. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Partial differential equations --- Dynamics. --- Ergodic theory. --- Partial differential equations. --- Mathematical physics. --- Mathematical analysis. --- Analysis (Mathematics). --- 517.1 Mathematical analysis --- Mathematical analysis --- Physical mathematics --- Physics --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics