# Beyond Partial Differential Equations

## On Linear and Quasi-Linear Abstract Hyperbolic Evolution Equations

Part of the Lecture Notes in Mathematics book series (LNM, volume 1898)

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Part of the Lecture Notes in Mathematics book series (LNM, volume 1898)

The present volume is self-contained and introduces to the treatment of linear and nonlinear (quasi-linear) abstract evolution equations by methods from the theory of strongly continuous semigroups. The theoretical part is accessible to graduate students with basic knowledge in functional analysis. Only some examples require more specialized knowledge from the spectral theory of linear, self-adjoint operators in Hilbert spaces. Particular stress is on equations of the hyperbolic type since considerably less often treated in the literature. Also, evolution equations from fundamental physics need to be compatible with the theory of special relativity and therefore are of hyperbolic type. Throughout, detailed applications are given to hyperbolic partial differential equations occurring in problems of current theoretical physics, in particular to Hermitian hyperbolic systems. This volume is thus also of interest to readers from theoretical physics.

Hilbert space abstract evolution equations functional analysis hyperbolic hyperbolic partial differential equation partial differential equation quasi-linear

- DOI https://doi.org/10.1007/978-3-540-71129-2
- Copyright Information Springer-Verlag Berlin Heidelberg 2007
- Publisher Name Springer, Berlin, Heidelberg
- eBook Packages Mathematics and Statistics
- Print ISBN 978-3-540-71128-5
- Online ISBN 978-3-540-71129-2
- Series Print ISSN 0075-8434
- Series Online ISSN 1617-9692
- Buy this book on publisher's site