Decay and Continuity of Boltzmann Equation in Bounded Domains

Boundaries occur naturally in kinetic equations and boundary effects are crucial for dynamics of dilute gases governed by the Boltzmann equation. We develop a mathematical theory to study the time decay and continuity of Boltzmann solutions for four basic types of boundary conditions: inflow, bounce-back reflection, specular reflection, and diffuse reflection. We establish exponential decay in $L^{\infty}$ norm for hard potentials for general classes of smooth domains near an absolute Maxwellian. Moreover, in convex domains, we also establish continuity for these Boltzmann solutions away from the grazing set of the velocity at the boundary. Our contribution is based on a new $L^{2}$ decay theory and its interplay with delicate $$ decay analysis for the linearized Boltzmann equation, in the presence of many repeated interactions with the boundary.Comment: 89 pages

Global classical solutions for partially dissipative hyperbolic system of balance laws

This work is concerned with ($N$-component) hyperbolic system of balance laws in arbitrary space dimensions. Under entropy dissipative assumption and the Shizuta-Kawashima algebraic condition, a general theory on the well-posedness of classical solutions in the framework of Chemin-Lerner's spaces with critical regularity is established. To do this, we first explore the functional space theory and develop an elementary fact that indicates the relation between homogeneous and inhomogeneous Chemin-Lerner's spaces. Then this fact allows to prove the local well-posedness for general data and global well-posedness for small data by using the Fourier frequency-localization argument. Finally, we apply the new existence theory to a specific fluid model-the compressible Euler equations with damping, and obtain the corresponding results in critical spaces.Comment: 39 page

The Einstein-Vlasov sytem/Kinetic theory

The main purpose of this article is to guide the reader to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades where the main focus has been on nonrelativistic- and special relativistic physics, e.g. to model the dynamics of neutral gases, plasmas and Newtonian self-gravitating systems. In 1990 Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. The Vlasov equation describes matter phenomenologically and it should be stressed that most of the theorems presented in this article are not presently known for other such matter models (e.g. fluid models). The first part of this paper gives an introduction to kinetic theory in non-curved spacetimes and then the Einstein-Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental in order to get a good comprehension of kinetic theory in general relativity.Comment: 31 pages. This article has been submitted to Living Rev. Relativity (http://www.livingreviews.org

l-Threonine Deaminase of Rhodospirillum rubrum

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65547/1/j.1432-1033.1971.tb01490.x.pd

The Einstein-Vlasov System/Kinetic Theory

The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein--Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on non-relativistic and special relativistic physics, i.e., to model the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the Einstein--Vlasov system. Since then many theorems on global properties of solutions to this system have been established.Comment: Published version http://www.livingreviews.org/lrr-2011-

Induction of DNA fragmentation by total-body irradiation in murine liver

Total-body irradiation (TBI) is an accepted modality to treat patients with disseminated tumors. The influence of the treatment on normal tissues is evaluated using mice by measuring the rate of the induction and distribution of apoptosis, as well as DNA fragmentation which occurs in the murine liver within hours of irradiation. Unanesthetized female C3H/He mice were exposed to y-ray TB1 of 2, 7, and 20 gray (Gy) delivered from 6 0 ~aot a dose rate of 114 cGy/min. Frozen sections of livers which were excised from the animals at various times after irradiation were stained by hematoxylin-eosin (H-E) to count numbers of apoptotic cells, or were examined to detect DNA fragmentation. The percentages of apoptotic cells and length of the period during which the maximum levels of the percentages were exhibited showed a dose-dependent increase in the sections stained with H-E. No positive cells for 3'-OH ends of fragmented DNA were found in the liver before TBI, whereas positive cells were observed immediately after irradiation without dosedependency, these positive cells returned to nearly basal levels after several hours. Positive cells were observed prior to showing apoptosis, suggesting that DNA fragmentation occurs immediately after TB1 independent of apoptosis. The difference in the time courses between induction of DNA fragmentation and of apoptosis was not observed in other organs or in the samples treated with the detergent. These results suggested that the 3'- OH ends newly generated by TB1 were masked by a detergent-soluble DNA-binding molecule which might be preferentially present in the murine liver