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This collection of original articles and surveys addresses the recent advances in linear and nonlinear aspects of the theory of partial differential equations. Key topics include: * Operators as "sums of squares" of real and complex vector fields: both analytic hypoellipticity and regularity for very low regularity coefficients; * Nonlinear evolution equations: Navier–Stokes system, Strichartz estimates for the wave equation, instability and the Zakharov equation and eikonals; * Local solvability: its connection with subellipticity, local solvability for systems of vector fields in Gevrey classes; * Hyperbolic equations: the Cauchy problem and multiple characteristics, both positive and negative results. Graduate students at various levels as well as researchers in PDEs and related fields will find this an excellent resource. List of contributors: L. Ambrosio N. Lerner H. Bahouri X. Lu S. Berhanu J. Metcalfe J.M. Bony T. Nishitani N. Dencker V. Petkov S. Ervedoza J. Rauch I. Gallagher M. Reissig J. Hounie L. Stoyanov E. Jannelli D. S. Tartakoff K. Kajitani D. Tataru A. Kurganov F. Treves G. Zampieri E. Zuazua.
Differential equations, Partial.  Microlocal analysis.  Differential equations, Partial  Microlocal analysis  Mathematics  Calculus  Physical Sciences & Mathematics  Partial differential equations  Mathematics.  Mathematical analysis.  Analysis (Mathematics).  Dynamics.  Ergodic theory.  Partial differential equations.  Functions of real variables.  Applied mathematics.  Engineering mathematics.  Physics.  Analysis.  Real Functions.  Dynamical Systems and Ergodic Theory.  Partial Differential Equations.  Mathematical Methods in Physics.  Applications of Mathematics.  Functional analysis  Global analysis (Mathematics).  Differentiable dynamical systems.  Differential equations, partial.  Mathematical physics.  Physical mathematics  Physics  Differential dynamical systems  Dynamical systems, Differentiable  Dynamics, Differentiable  Differential equations  Global analysis (Mathematics)  Topological dynamics  Math  Science  Analysis, Global (Mathematics)  Differential topology  Functions of complex variables  Geometry, Algebraic  Engineering  Engineering analysis  Mathematical analysis  Natural philosophy  Philosophy, Natural  Physical sciences  Dynamics  Ergodic transformations  Continuous groups  Mathematical physics  Measure theory  Transformations (Mathematics)  Dynamical systems  Kinetics  Mechanics, Analytic  Force and energy  Mechanics  Statics  Real variables  517.1 Mathematical analysis
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This collection of original articles and surveys, emerging from a 2011 conference in Bertinoro, Italy, addresses recent advances in linear and nonlinear aspects of the theory of partial differential equations (PDEs). Phase space analysis methods, also known as microlocal analysis, have continued to yield striking results over the past years and are now one of the main tools of investigation of PDEs. Their role in many applications to physics, including quantum and spectral theory, is equally important. Key topics addressed in this volume include: *general theory of pseudodifferential operators *Hardytype inequalities *linear and nonlinear hyperbolic equations and systems *Schrödinger equations *waterwave equations *EulerPoisson systems *NavierStokes equations *heat and parabolic equations Various levels of graduate students, along with researchers in PDEs and related fields, will find this book to be an excellent resource. Contributors T. Alazard P.I. Naumkin J.M. Bony F. Nicola N. Burq T. Nishitani C. Cazacu T. Okaji J.Y. Chemin M. Paicu E. Cordero A. Parmeggiani R. Danchin V. Petkov I. Gallagher M. Reissig T. Gramchev L. Robbiano N. Hayashi L. Rodino J. Huang M. Ruzhanky D. Lannes J.C. Saut F. Linares N. Visciglia P.B. Mucha P. Zhang C. Mullaert E. Zuazua T. Narazaki C. Zuily.
Differential equations, Partial.  Global analysis (Mathematics).  Mathematics.  Phase space (Statistical physics).  Phase space (Statistical physics)  Differential equations, Partial  Mathematics  Physical Sciences & Mathematics  Calculus  Partial differential equations  Space, Phase (Statistical physics)  Mathematical analysis.  Analysis (Mathematics).  Dynamics.  Ergodic theory.  Differential equations.  Partial differential equations.  Applied mathematics.  Engineering mathematics.  Mathematical physics.  Partial Differential Equations.  Dynamical Systems and Ergodic Theory.  Mathematical Physics.  Ordinary Differential Equations.  Analysis.  Applications of Mathematics.  Generalized spaces  Differential equations, partial.  Differentiable dynamical systems.  Differential Equations.  Math  Science  Analysis, Global (Mathematics)  Differential topology  Functions of complex variables  Geometry, Algebraic  517.91 Differential equations  Differential equations  Differential dynamical systems  Dynamical systems, Differentiable  Dynamics, Differentiable  Global analysis (Mathematics)  Topological dynamics  Physical mathematics  Physics  Ergodic transformations  Continuous groups  Mathematical physics  Measure theory  Transformations (Mathematics)  Dynamical systems  Kinetics  Mechanics, Analytic  Force and energy  Mechanics  Statics  Engineering  Engineering analysis  Mathematical analysis  517.1 Mathematical analysis
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This collection of original articles and surveys treats linear and nonlinear aspects of the theory of partial differential equations. Phase space analysis methods, also known as microlocal analysis, have yielded striking results over the past years and have become one of the main tools of investigation. Equally important is their role in many applications to physics, for example, in quantum and spectral theory. Key topics: * The Cauchy problem for linear and nonlinear hyperbolic equations * Scattering theory * Inverse problems * Hyperbolic systems * Gevrey regularity of solutions of PDEs * Analytic hypoellipticity and unique features: * Original articles are selfcontained with full proofs * Survey articles give a quick and direct introduction to selected topics evolving at a fast pace Graduate students at various levels as well as researchers in PDEs and related fields will find this an excellent resource.
Differential equations, Partial  Phase space (Statistical physics)  Space, Phase (Statistical physics)  Mathematics.  Dynamics.  Ergodic theory.  Partial differential equations.  Applied mathematics.  Engineering mathematics.  Physics.  Quantum optics.  Partial Differential Equations.  Mathematical Methods in Physics.  Applications of Mathematics.  Quantum Optics.  Dynamical Systems and Ergodic Theory.  Generalized spaces  Differential equations, partial.  Mathematical physics.  Differentiable dynamical systems.  Math  Science  Differential dynamical systems  Dynamical systems, Differentiable  Dynamics, Differentiable  Differential equations  Global analysis (Mathematics)  Topological dynamics  Physical mathematics  Physics  Partial differential equations  Mathematics  Ergodic transformations  Continuous groups  Mathematical physics  Measure theory  Transformations (Mathematics)  Dynamical systems  Kinetics  Mechanics, Analytic  Force and energy  Mechanics  Statics  Optics  Photons  Quantum theory  Engineering  Engineering analysis  Mathematical analysis  Natural philosophy  Philosophy, Natural  Physical sciences  Dynamics
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The book collects the most relevant results from the INdAM Workshop "Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics" held in Rome, September 1418, 2015. The contributions discuss recent major advances in the study of nonlinear hyperbolic systems, addressing general theoretical issues such as symmetrizability, singularities, low regularity or dispersive perturbations. It also investigates several physical phenomena where such systems are relevant, such as nonlinear optics, shock theory (stability, relaxation) and fluid mechanics (boundary layers, water waves, Euler equations, geophysical flows, etc.). It is a valuable resource for researchers in these fields. .
Nonlinear systems.  Exponential functions.  Functions, Exponential  Hyperbolic functions  Systems, Nonlinear  Mathematics.  Fourier analysis.  Partial differential equations.  Applied mathematics.  Engineering mathematics.  Mathematical physics.  Partial Differential Equations.  Fourier Analysis.  Mathematical Physics.  Applications of Mathematics.  Exponents (Algebra)  Logarithms  Transcendental functions  System theory  Differential equations, partial.  Math  Science  Analysis, Fourier  Mathematical analysis  Partial differential equations  Engineering  Engineering analysis  Physical mathematics  Physics  Mathematics
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