本书是现代应用数学丛书中的一本，主要对非线性双曲型方程的一些问题与应用知识作了介绍。全书分为两部分：强非线性等离子体模型中的数学与数值分析(Mathematical and Numerical Analysis for Strongly Nonlinear Plasma Models)，拟线性双曲线系统的精确可控性和可观察性及其应用(Exact Controllability and Observability for Quasilinear Hyperbolic Systems and Applications)。该书可供各大专院校作为教材使用，也可供从事相关工作的人员作为参考用书使用。

This volume is composed of two parts: Mathematical and Numerical Analysis for Strongly Nonlinear Plasma Models and Exact Controllability and Observability for Quasilinear Hyperbolic Systems and Applications. It presents recent progress and results obtained in the domains related to both subjects without attaching much importance to the details of proofs but rather to difficulties encountered, to open problems and possible ways to be exploited. It will be very useful for promoting further study on some important problems in the future.

Part Ⅰ  Mathematical and Numerical Analyses of Strongly Nonlinear Plasma Models

 Open Boundary Conditions and Computational Schemes for Schr5dinger Equations with General Potentials and Nonlinearities

 On Hydrodynamic Models for LEO Spacecraft Charging

 Asymptotic Regimes for Plasma Physics with Strong Magnetic Fields

 The Zero-Electron-Mass Limit in the Hydrodynamic Model (Euler-Poisson System)

 Modeling and Simulation of Fluid-Particles Flows

 Well-Posedness and Stability of Quantum Hydrodynamics for Semiconductors in Ra

 Bloch Decomposition-Based Method for High Frequency Waves in Periodic Media

 Some Results of the Euler-Poisson System for Plasmas and Semiconductors

 Behavior of Discontinuities in Thermoelasticity with Second Sound

 The Convergence of Euler-Poisson System to the Incompressible Euler Equations

 On the Relaxation-time Limits in Bipolar Hydrodynamic Models for Semiconductors

Part Ⅱ Exact Controllability and Observability for

 Quasilinear Hyperbolic Systems and Applications

 Observability in Arbitrary Small Time for Discrete Approximations of Conservative Systems

 Logarithmic Decay of Hyperbolic Equations with Arbitrary Small

 Boundary Damping

 A Remark on the Controllability of a System of Conservation Laws in the Context of Entropy Solutions

 Introduction to the Control of PDE's

 Exact Controllability and Exact Observability for Quasilinear Hyperbolic Systems: Known Results and Open Problems

 Waves, Damped Wave and Observation

 Control Problems for Fluid Equations

 Global Existence of a Degenerate Kirchhoff System with Boundary Dissipation

 Remarks on the Controllability of Some Quasilinear Equations