摘要:

It came as a sudden, unexpected shock to Marvin Shinbrot's many friends and co-workers around the globe when the news of his death spread after September lath, 1987. Few had known that he was ill, and hardly anybody suspected the seriousness of his lung problem. He had clearly decided not to burden his friends with his condition and to continue to live a normal life for as long as possible- and he did so until the very last day. The summer of 87 saw him teach an extra heavy load; he kept working on many scientific projects, and his contagious enthusiasm for mathematics was unabated. Friends and colleagues received scientific mail from him days after his death.

ISSN:0041-1450    

DOI:10.1080/00411458908214495

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Release a statistically correlated set of molecules into space. Presumably, their thermal motion quickly destroys the correlation and the whole collection then degenerates to equilibrium, following their description by the Boltzmann equation. There 1s no known proof of this, and the main point of this paper is to supply one in a simple case.

ISSN:0041-1450    

DOI:10.1080/00411458908214496

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

In the first part of the paper, for the three dimensional Broadwell model, we construct (2+1)-dimensional (two spatial coordinates plus time) semi-periodic exact solutions. As usual such solutions are sums of similarity shock waves solutions. These semi-periodic solutions represent periodic waves submitted to a strong perturbation and rebuilt after the shock. To this aim we build up positive periodic (1+1)-dimensional solutions with a time dependence and add a component which is a real similarity shock-wave. For the whole solution we choose the time dependence of the periodic part such that the positivity problem is reduced to the positivity of the shock component. These solutions depend on two arbitrary parameters and we prove that there exists a domain for which the constructed solutions are positive.

ISSN:0041-1450    

DOI:10.1080/00411458908214497

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

We study the relation between the statistical solutions of the Boltzmann equation and the Boltzmann hierarchy, and prove an uniqueness theorem for the solution to the Boltzmann hierarchy for initial data near the equilibrium.

ISSN:0041-1450    

DOI:10.1080/00411458908214498

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

It is shown that the number of collisions in a system of finitely many hard spheres, which interact through elastic collisions but move freely otherwise in all of 3 R3, is finite.

ISSN:0041-1450    

DOI:10.1080/00411458908214499

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

This paper deals with the analysis of the initial value problem for the Boltzmann equation in the presence of an external force field. The problem is first dealt with in full generality: mild formulation and estimates suitable to provide global existence results of the solution to the initial value problem. Then global existence is proven for force fields integrable, in time, with respect to a constant force field.

ISSN:0041-1450    

DOI:10.1080/00411458908214500

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The concept of mechanical reversibility finds a natural generalization to general dynamical systems by the so-called “S-reversibility”. This reversibility concept is discussed from a mathematical point of view. For abstract dynamical systems a Hilbert space characterization of S-reversibility is given, and the results are interpreted from a physical point of view.

ISSN:0041-1450    

DOI:10.1080/00411458908214501

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Nonlinear transport equations are studied, in which the nonlincarity, arising from the collision operator, is well behaved in the weak* topology of a weakly compactly generated Banach space. The Cauchy problem is posed for general semilinear evolution equations, which can model a variety of diffusion and kinetic equations. Local existence theorems are obtained for such spaces. In particular, the results are applicable to transport equations inL∞with appropriate weak* (i.e., L1) continuity properties.

ISSN:0041-1450    

DOI:10.1080/00411458908214502

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

A few steady solutions of the linearized Boltzmann equation are discussed, under the assuption that the molecules reverse their speed when colliding against a wall, a boundary condition introduced by Schnute and recently applied to fluid flow simulation by cellular automata.

ISSN:0041-1450    

DOI:10.1080/00411458908214503

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

Familiar nonstandard methods are used to prove that the Loeb solutions for the Boltzmann equation in *Rngenerate measure valued solutions on Rn.

ISSN:0041-1450    

DOI:10.1080/00411458908214504

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor