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Microlocal analysis --- Analyse microlocale --- Fonctions de variables complexes

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This volume contains 23 articles on algebraic analysis of differential equations and related topics, most of which were presented as papers at the conference ""Algebraic Analysis of Differential Equations - from Microlocal Analysis to Exponential Asymptotics"" at Kyoto University in 2005. This volume is dedicated to Professor Takahiro Kawai, who is one of the creators of microlocal analysis and who introduced the technique of microlocal analysis into exponential asymptotics.

Mathematics. --- Integral Transforms, Operational Calculus. --- Ordinary Differential Equations. --- Partial Differential Equations. --- Special Functions. --- Integral Transforms. --- Differential Equations. --- Differential equations, partial. --- Functions, special. --- Mathématiques --- Differential equations. --- Mathematical analysis. --- Differential equations --- Mathematical analysis --- Mathematics --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Operations Research --- Calculus --- 517.1 Mathematical analysis --- 517.91 Differential equations --- Integral transforms. --- Operational calculus. --- Partial differential equations. --- Special functions. --- Special functions --- Partial differential equations --- Operational calculus --- Electric circuits --- Integral equations --- Transform calculus --- Transformations (Mathematics) --- Math --- Science

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This book is designed to present some recent results on some nonlinear parabolic-hyp- bolic coupled systems arising from physics, mechanics and material science such as the compressible Navier-Stokes equations, thermo(visco)elastic systems and elastic systems. Some of the content of this book is based on research carried out by the author and his collaborators in recent years. Most of it has been previously published only in original papers,andsomeofthematerialhasneverbeenpublisheduntilnow.Therefore,theauthor hopes that the book will bene?t both the interested beginner in the ?eld and the expert. AllthemodelsunderconsiderationinChapters2-10arebuiltonnonlinearevolution equations that are parabolic-hyperbolic coupled systems of partial differential equations with time t as one of the independentvariables. This type of partial differential equations arises not only in many ?elds of mathematics, but also in other branches of science such as physics, mechanics and materials science, etc. For example, some models studied in this book, such as the compressible Navier-Stokes equations (a 1D heat conductive v- cous real gas and a polytropic ideal gas) from ?uid mechanics, and thermo(visco)elastic systemsfrommaterialsscience, are typicalexamplesof nonlinearevolutionaryequations. It is well known that the properties of solutions to nonlinear parabolic-hyperbolic coupledsystems are very different from those of parabolicor hyperbolicequations. Since the 1970s,more andmore mathematicianshave begunto focustheir interests onthe study of local well-posedness, global well-posedness and blow-up of solutions in a ?nite time.

Operator theory --- Partial differential equations --- differentiaalvergelijkingen --- analyse (wiskunde)