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