Optimal Decay Estimates on the Linearized Boltzmann Equation with Time Dependent Force and their Applications

2007 ◽  
Vol 277 (1) ◽  
pp. 189-236 ◽  
Author(s):  
Renjun Duan ◽  
Seiji Ukai ◽  
Tong Yang ◽  
Huijiang Zhao
Keyword(s):  
Boltzmann Equation ◽  
Time Dependent ◽  
Decay Estimates ◽  
Linearized Boltzmann Equation ◽  
Optimal Decay

Solution of the Boltzmann equation for electrons in external electric fields

1970 ◽  
Vol 4 (1) ◽  
pp. 145-159 ◽  
Author(s):  
L. Stenflo
Keyword(s):  
Wave Propagation ◽  
Boltzmann Equation ◽  
Electric Fields ◽  
Transverse Wave ◽  
Analytical Solutions ◽  
Density Fluctuation ◽  
Time Dependent ◽  
Exact Analytical Solutions ◽  
External Electric Fields ◽  
Linearized Boltzmann Equation

A plasma in a time-dependent external electric field is considered. Collisions are described by means of Fokker—Planck and BGK models. Longitudinal and transverse wave propagation is treated by means of exact analytical solutions of the linearized Boltzmann equation. The results generalize previous calculations on dispersion relations and density fluctuation spectra.

Numerical Analysis of the Time-Dependent Energy and Momentum Transfers in a Rarefied Gas Between Two Parallel Planes Based on the Linearized Boltzmann Equation

2010 ◽  
Vol 133 (2) ◽  
Author(s):  
Toshiyuki Doi
Keyword(s):  
Energy Transfer ◽  
Boltzmann Equation ◽  
Rarefied Gas ◽  
Numerical Data ◽  
Time Dependent ◽  
Sound Waves ◽  
Low Frequencies ◽  
Resonance Effects ◽  
Linearized Boltzmann Equation ◽  
Wide Range

Periodic time-dependent behavior of a rarefied gas between two parallel planes caused by an oscillatory heating of one plane is numerically studied based on the linearized Boltzmann equation. Detailed numerical data of the energy transfer from the heated plane to the unheated plane and the forces of the gas acting on the boundaries are provided for a wide range of the gas rarefaction degree and the oscillation frequency. The flow is characterized by a coupling of heat conduction and sound waves caused by repetitive expansion and contraction of the gas. For a small gas rarefaction degree, the energy transfer is mainly conducted by sound waves, except for very low frequencies, and is strongly affected by the resonance of the waves. For a large gas rarefaction degree, the resonance effects become insignificant and the energy transferred to the unheated plane decreases nearly monotonically as the frequency increases. The force of the gas acting on the heated boundary shows a remarkable minimum with respect to the frequency even in the free molecular limit.

scholarly journals Global existence and decay estimates for nonlinear wave equations with space-time dependent dissipative term

2015 ◽  
Vol 12 (02) ◽  
pp. 249-276
Author(s):  
Tomonari Watanabe
Keyword(s):  
Global Existence ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Space Time ◽  
Time Dependent ◽  
Nonlinear Wave Equations ◽  
Energy Estimates ◽  
Space Region ◽  
Decay Estimates ◽  
Dissipative Term

We study the global existence and the derivation of decay estimates for nonlinear wave equations with a space-time dependent dissipative term posed in an exterior domain. The linear dissipative effect may vanish in a compact space region and, moreover, the nonlinear terms need not be in a divergence form. In order to establish higher-order energy estimates, we introduce an argument based on a suitable rescaling. The proposed method is useful to control certain derivatives of the dissipation coefficient.

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