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Zusatztext With an extensive bibliography including classical and recent papers both in PDE analysis and in applications (mainly to gas dynamics), this text will be valuable to graduates and researchers in both hyperbolic PDEs and compressible fluid dynamics. Klappentext Authored by leading scholars, this comprehensive, self-contained text presents a view of the state of the art in multi-dimensional hyperbolic partial differential equations, with a particular emphasis on problems in which modern tools of analysis have proved useful. Ordered in sections of gradually increasing degrees of difficulty, the text first covers linear Cauchy problems and linear initial boundary value problems, before moving on to nonlinear problems, including shock waves. The book finishes with a discussion of the application of hyperbolic PDEs to gas dynamics, culminating with the shock wave analysis for real fluids. With an extensive bibliography including classical and recent papers both in PDE analysis and in applications (mainly to gas dynamics), this text will be valuable to graduates and researchers in both hyperbolic PDEs and compressible fluid dynamics. Zusammenfassung Authored by leading scholars, this text presents the state of the art in multi-dimensional hyperbolic PDEs, with an emphasis on problems in which modern tools of analysis are used. Ordered in sections of gradually increasing difficulty and with an extensive bibliography, the text is ideal for graduates and researchers in applied mathematics. Inhaltsverzeichnis Preface Introduction Notations The linear Cauchy problem 1: Linear Cauchy problem with constant coefficients 2: Linear Cauchy problem with variable coefficients The linear initial boundary value problem 3: Friedrichs symmetric dissipative IBVPs 4: Initial boundary value problem in a half-space with constant coefficients 5: Construction of a symmetrizer under (UKL) 6: The characteristic IBVP 7: The homogeneous IBVP 8: A classification of linear IBVPs 9: Variable coefficients initial boundary value problems Nonlinear problems 10: The Cauchy problem for quasilinear systems 11: The mixed problem for quasilinear systems 12: Persistence of multidimensional shocks Applications to gas dynamics 13: The Euler equations for real fluids 14: Boundary conditions for Euler equations 15: Shock stability in gas dynamics Appendix A: Basic calculus results B: Fourier and Laplace analysis C: Pseudo/para-differential calculus Bibliography Index ...
