Weak solutions of the Boltzmann equation equation and energy conservation
نویسندگان
چکیده
منابع مشابه
Infinite Energy Solutions to the Homogeneous Boltzmann Equation
The goal of this work is to present an approach to the homogeneous Boltzmann equation for Maxwellian molecules with a physical collision kernel which allows us to construct unique solutions to the initial value problem in a space of probability measures defined via the Fourier transform. In that space, the second moment of a measure is not assumed to be finite, so infinite energy solutions are ...
متن کاملShock Profile Solutions of the Boltzmann Equation*
Shock waves in gas dynamics can be described by the Euler Nav ie r Stokes, or Boltzmann equations. We prove the existence of shock profile solutions of the Boltzmann equation for shocks which are weak. The shock is written as a truncated expansion in powers of the shock strength, the first two terms of which come exactly from the Taylor tanh (x) profile for the Navie r Stokes solution. The full...
متن کاملInterfacial Solutions of the Poisson-Boltzmann Equation
The linearized Poisson-Boltzmann equation is considered for boundary conditions corresponding to a fixed point-charge ion near the planar boundary between an electrolytic solution and a dielectric substrate. Use of the Fourier expansion for this fixed charge density allows the mean potential to be synthesized in the form of a simple quadrature. Subsequently, it is possible to compute the revers...
متن کاملSolutions of the Linear Boltzmann Equation and Some Dirichlet Series
Abstract. It is shown that a broad class of generalized Dirichlet series (including the polylogarithm, related to the Riemann zeta-function) can be presented as a class of solutions of the Fourier transformed spatially homogeneous linear Boltzmann equation with a special Maxwell-type collision kernel. The result is based on an explicit integral representation of solutions to the Cauchy problem ...
متن کاملOn Weak Solutions to the Linear Boltzmann Equation with Inelastic Coulomb Collisions
Abstract. This paper considers the timeand space-dependent linear Boltzmann equation with general boundary conditions in the case of inelastic (granular) collisions. First, in the (angular) cut-off case, mild L1-solutions are constructed as limits of the iterate functions and boundedness of higher velocity moments are discussed in the case of inverse power collisions forces. Then the problem of...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 1995
ISSN: 0893-9659
DOI: 10.1016/0893-9659(95)00011-e