摘要:

Existence theorems have been recently proved by several authors for the initial-boundary value problem for the nonlinear Boltzmann equation. Here we discuss and extend these results.

ISSN:0041-1450    

DOI:10.1080/00411459608220711

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

We prove that the solution of the space homogeneous Boltzmann equation is bounded from below by an exponential C exp{– ―v ―2+λ}, where λ > 0 is arbitrary. The estimate holds uniformly for all t ≥ to, where tois a given positive time.

ISSN:0041-1450    

DOI:10.1080/00411459608220712

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

In this paper, we investigate the boundary layer behavior of solutions to the one dimensional Broadwell model of the nonlinear Boltzmann equation for small mean free path. We consider the analogue of Maxwell's diffusive and the reflexive boundary conditions. It is found that even for such a simple model, there are boundary layers due to purely kinetic effects which cannot be detected by the corresponding Navier-Stokes system. It is also found numerically that a compressive boundary layer is not always stable in the sense that it may detach from the boundary and move into the interior of the gas as a shock layer.

ISSN:0041-1450    

DOI:10.1080/00411459608220713

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

A stable finite element scheme for advection dominated problems is presented. The method is based on a classical piecewise linear continuous approximation of the solution and is proved to verify the discrete maximum principle whenever the triangulation is of weakly acute type. Several numerical tests confirm robustness of the method.

ISSN:0041-1450    

DOI:10.1080/00411459608220714

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

We prove that the dynamical evolution of an elasto-plastic material with so-called isotropic hardening has a unique and global generalized solution in the spaceL2. This solution satisfies the correct system of equations if it is piecewise smooth and only has discontinuities in the elastic region, which is natural in this model. This solution is obtained, at least in the regular case, as the zero-relaxation limit of a corresponding elastic viscoplastic material, and satisfies in any case the system (2.1)(2.2) below, which in the plastic regime (as long as we keep loading) turns out to be the system of nonlinear elasticity.

ISSN:0041-1450    

DOI:10.1080/00411459608220715

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

We study the one-dimensional free streaming operator in a slab domain with general boundary conditions described by a linear positive operator Λ. Under the assumptions that Λ−1exists and is positive and the free streaming operator TΛis resolvent positive, we prove that TΛis the infinitesimal generator of a positive strongly continuous semigroup, which is contractive if ∥ Λ ∥ ≤ 1 and quasi-bounded if ∥ Λ > 1 and ∥ Λ−1≤ ∥ 1. We give also the mathematical definition of dissipative, conservative and multiplying boundary walls in terms of Λ, and we show how these properties of the boundary walls can affect the type of the semigroup generated by TΛ.

ISSN:0041-1450    

DOI:10.1080/00411459608220716

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

We show existence of solutions to an infinite system of parabolic equations obtained by adding spatial diffusion to the classical coagulation-fragmentation equations. In the case where the spatial diffusion coefficients depend on cluster size, local existence is shown. A global solution is obtained in the case where all the diffusivities are equal. As done in previous studies on the coagulation-fragmentation system, the method of proof relies on the truncation of the infinite system; essential in the derivation of the necessary estimates is the fact that the total concentration of particles satisfies a parabolic equation, to which the maximum principle can be applied.

ISSN:0041-1450    

DOI:10.1080/00411459608220717

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

We propose a numerical approximation to kinetic equations of Boltzmann type based on the splitting in time between the transport and the collision phases. By means of the representation of the solution to the relaxation part as an arithmetic mean of the convolution iterates of a quadratic positive operator, we construct a stable discretization valid for arbitrary values of the mean free path. Comparison of the present approximation with previous ones is made for Broadwell discrete velocity model.

ISSN:0041-1450    

DOI:10.1080/00411459608220718

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

ISSN:0041-1450    

DOI:10.1080/00411459608220719

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

ISSN:0041-1450    

DOI:10.1080/00411459608220720

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor