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Differential equations, Nonlinear --- Fluid dynamics --- Heat --- Equations différentielles non linéaires --- Fluides, Dynamique des --- Numerical solutions --- Convection --- Mathematical models --- Solutions numériques --- Fluid dynamics. --- Numerical solutions. --- Mathematical models. --- Equations différentielles non linéaires --- Solutions numériques --- Differential equations, Nonlinear - Numerical solutions --- Heat - Convection - Mathematical models

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The topic of the 2010 Abel Symposium, hosted at the Norwegian Academy of Science and Letters, Oslo, was Nonlinear Partial Differential Equations, the study of which is of fundamental importance in mathematics and in almost all of natural sciences, economics, and engineering. This area of mathematics is currently in the midst of an unprecedented development worldwide. Differential equations are used to model phenomena of increasing complexity, and in areas that have traditionally been outside the realm of mathematics. New analytical tools and numerical methods are dramatically improving our understanding of nonlinear models. Nonlinearity gives rise to novel effects reflected in the appearance of shock waves, turbulence, material defects, etc., and offers challenging mathematical problems. On the other hand, new mathematical developments provide new insight in many applications. These proceedings present a selection of the latest exciting results by world leading researchers.

Differential equations, Nonlinear -- Numerical solutions. --- Differential equations, Nonlinear. --- Nonlinear mechanics -- Mathematics. --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Differential equations, Nonlinear --- Differential equations --- 517.91 Differential equations --- Mathematics. --- Partial differential equations. --- Physics. --- Partial Differential Equations. --- Mathematical Methods in Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Partial differential equations --- Math --- Science --- Differential equations, partial. --- Mathematical physics. --- Physical mathematics --- Physics

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This volume contains the texts of the four series of lectures presented by B.Cockburn, C.Johnson, C.W. Shu and E.Tadmor at a C.I.M.E. Summer School. It is aimed at providing a comprehensive and up-to-date presentation of numerical methods which are nowadays used to solve nonlinear partial differential equations of hyperbolic type, developing shock discontinuities. The most effective methodologies in the framework of finite elements, finite differences, finite volumes spectral methods and kinetic methods, are addressed, in particular high-order shock capturing techniques, discontinuous Galerkin methods, adaptive techniques based upon a-posteriori error analysis.

Differential equations, Hyperbolic --- Differential equations, Nonlinear --- Numerical solutions --- Congresses --- Differential equations [Hyperbolic] --- Differential equations [Nonlinear ] --- Partial differential equations. --- Numerical analysis. --- Thermodynamics. --- Computational intelligence. --- Partial Differential Equations. --- Numerical Analysis. --- Computational Intelligence. --- Chemistry, Physical and theoretical --- Dynamics --- Mechanics --- Physics --- Heat --- Heat-engines --- Quantum theory --- Mathematical analysis --- Partial differential equations --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Differential equations, Hyperbolic - Numerical solutions - Congresses --- Differential equations, Nonlinear - Numerical solutions - Congresses

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Numerical solutions of differential equations --- Mathematical physics --- Differential geometry. Global analysis --- Differential equations, Nonlinear --- Differentiable dynamical systems --- Averaging method (Differential equations) --- Equations différentielles non linéaires --- Dynamique différentiable --- Méthode des moyennes (Equations différentielles) --- Numerical solutions --- Solutions numériques --- Differentiable dynamical systems. --- Numerical solutions. --- Averaging method (Differential equations). --- Equations différentielles non linéaires --- Dynamique différentiable --- Méthode des moyennes (Equations différentielles) --- Solutions numériques --- Numerical analysis --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Method of averaging (Differential equations) --- Differential equations, Nonlinear - Numerical solutions

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B. Coleman, M.E. Gurtin: Thermodynamics and wave propagation in Elastic and Viscoelastic media.- L. De Vito: Sui fondamenti della meccanica di sistemi continui (II).- G. Fichera: Problemi elastostatici con ambigue condizioni al contorno.- G. Grioli: Sistemi a trasformazioni reversibili.- W. Noll: the foundations of mechanics.- R.A. Toupin: Elasticity and electromagnetic.- C.C. Wang: Subfluids.

Continuum mechanics. --- Differential equations, Nonlinear -- Numerical solutions. --- Nonlinear theories. --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Calculus --- Applied Mathematics --- Mathematical Theory --- Continuity. --- Continuum --- Mathematics. --- Partial differential equations. --- Thermodynamics. --- Microwaves. --- Optical engineering. --- Partial Differential Equations. --- Continuum Mechanics and Mechanics of Materials. --- Microwaves, RF and Optical Engineering. --- Indivisibles (Philosophy) --- Philosophy --- Differential equations, partial. --- Mechanics. --- Mechanics, Applied. --- Solid Mechanics. --- Partial differential equations --- Hertzian waves --- Electric waves --- Electromagnetic waves --- Geomagnetic micropulsations --- Radio waves --- Shortwave radio --- Chemistry, Physical and theoretical --- Dynamics --- Mechanics --- Physics --- Heat --- Heat-engines --- Quantum theory --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Mechanical engineering