摘要:

We study in this paper one-dimensional probe models. Mathematically, we are faced with a singular perturbation problem for a two-species Vlasov-Poisson system. We show that the solution presents two boundary layers which are fully analyzed. We also study a modified model which eliminates the probe boundary layer.

ISSN:0041-1450    

DOI:10.1080/00411459608220701

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

A set of closed hydrodynamic-like equations is derived from Boltzmann's transport equation (BTE) describing charge transport in semiconductors. The moment hierarchy is closed by using the entropy principle and the production terms are modeled as relaxation terms consistently with the Onsager Reciprocity Principle. Finally the model is compared with Monte Carlo simulations for silicon.

ISSN:0041-1450    

DOI:10.1080/00411459608220702

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

The paper claims to give a systematic approach allowing one to obtain invertible variable transformations mapping nonlinear partial differential equations either into autonomous or linear form provided that some suitable conditions are satisfied. The procedure makes use of Lie group analysis so that some symmetries are required in order to obtain the required transformations, which are related to canonical variables. A linearization procedure is given in the last part of the paper valid for systems of partial differential equations that can be reduced to a single nonlinear equation linearly degenerate. The procedures are explained with some examples of physical interest

ISSN:0041-1450    

DOI:10.1080/00411459608220703

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Some stability results for hyperbolic and parabolic P. D.Es. are presented and recent results are reviewed. The Liapunov direct method is used.

ISSN:0041-1450    

DOI:10.1080/00411459608220704

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

In this paper we present the application of an adaptive wavelet method to the numerical solution of the viscous Burgers equation. Unlike other approaches6,7, such a method is based on a collocation technique. The properties of wavelet bases are exploited in order to adaptively design the grid at each time-step. Numerical results are presented for several 1-D test problems with small viscosity.

ISSN:0041-1450    

DOI:10.1080/00411459608220705

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

In this paper we study the long-time behaviour of the solutions of the linear Boltzmann equation for charged particles in a three dimensional spatially homogeneous system under the influence of an external electric field and in the presence of a source term. The runaway phenomenon and the decay to steady state solutions are considered. Finally we formally derive and study the equation for the non-equilibrium steady state distribution in the presence of a time independent source.

ISSN:0041-1450    

DOI:10.1080/00411459608220706

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

A numerical method for the solution of the spatially homogeneous Boltzmann equation is proposed. The scheme is based first in expanding the distribution function in Fourier series, then in finite difference discretizing in time and velocity space. This allows an accurate evaluation of the collision operator with a reduced computational cost. Moreover, for a class of collision kernels, this approach leads to a quadrature formula that can be computed through a fast algorithm. First results on a twodimensional problem confirm the efficiency of the method.

ISSN:0041-1450    

DOI:10.1080/00411459608220707

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

We extend in this work previous results of regularization for the spatially homogeneous non cutoff 2D radially symmetric Boltzmann equation which held only in the case of Maxwellian molecules. Velocity dependent cross sections can now be taken in account.

ISSN:0041-1450    

DOI:10.1080/00411459608220708

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

A stabilized finite element method for the approximation of advection-diffusion equations is presented. The stabilization is obtained through the enlargement of the classical finite element spaces with suitable bubble functions. The resulting scheme is shown to be equivalent to the Streamline-Upwind Petrov/Galerkin method.

ISSN:0041-1450    

DOI:10.1080/00411459608220709

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

We analyze closure conditions in the small initial temperature limit for classical and quantum mechanical moment hierarchies of corresponding collisionless kinetic equations. Euler equations with a nondiagonal pressure tensor are obtained in the classical case. In the quantum case we consider the cases of fixed and small (scaled) Planck constant and derive Quantum Hydrodynamic equations.

ISSN:0041-1450    

DOI:10.1080/00411459608220710

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor