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1. 1. Two Problems on Existence and Approximation Related to the Boltzmann Equation

   Författare :Vladislav Panferov; Göteborgs universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Boltzmann equation; Povzner type models; diffuse reflection; discrete-velocity models; existence for large data; weak compactness; consistency; convergence; diffuse reflection;

   Sammanfattning : In this thesis, two different types of problems related to the Boltzmann equation of kinetic theory are studied. The first part is devoted to establishing consistency and convergence for discrete-velocity models of the Boltzmann equation. For a new such model, introduced by the author jointly with A. LÄS MER

3. 2. Propagation of Chaos for Kac-like Particle Systems

   Författare :Dawan Mustafa; Göteborgs universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Master equations; chaotic densities; kinetic equations; propagation of chaos; Kac model; thermostatted master equation; Boltzmann equation; BGK equation; quenched process; uniform distribution; spectral gap; approximation process; kinetic equations;

   Sammanfattning : This thesis concerns various aspects of the Kac model. The Kac model is a Markov jump process for a particle system where the total kinetic energy of the system is conserved. This particle model is connected to a limiting equation, describing the evolution of a one-particle density, when the numbers of particles tends to infinity. LÄS MER

4. 3. On Half-Space and Shock-Wave Problems for Discrete Velocity Models of the Boltzmann Equation

   Författare :Niclas Bernhoff; Alexander Bobylev; Giuseppe Toscani; Karlstads universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Boltzmann equation; discrete velocity models; boundary value problems; shock waves; MATHEMATICS; MATEMATIK; Matematik; Mathematics;

   Sammanfattning : We study some questions related to general discrete velocity (with arbitrarily number of velocities) models (DVMs) of the Boltzmann equation. In the case of plane stationary problems the typical DVM reduces to a dynamical system (system of ODEs). Properties of such systems are studied in the most general case. LÄS MER

5. 4. Kinetic modelling of runaway in plasmas

   Författare :Ola Embréus; Chalmers tekniska högskola; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Fokker-Planck equation; synchrotron radiation; plasma; runaway; bremsstrahlung; Boltzmann equation;

   Sammanfattning : The phenomenon of runaway occurs in plasmas in the presence of a strong electric field, which overcomes the collisional friction acting on the charged particles moving through the plasma. A subpopulation of particles can then be accelerated to energies significantly higher than the thermal energy. LÄS MER

7. 5. Kinetic modelling of runaways in plasmas

   Författare :Ola Embréus; Chalmers tekniska högskola; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; runaway; Fokker-Planck equation; tokamak; Boltzmann equation; positrons; bremsstrahlung; plasma; synchrotron radiation;

   Sammanfattning : The phenomenon of runaway occurs in plasmas in the presence of a strong electric field, when the accelerating force overcomes the collisional friction acting on the charged particles moving through the plasma. Electron runaway is observed in both laboratory and space plasmas, and is of great importance in fusion-energy research, where the energetic electrons can damage the plasma-facing components of fusion reactors. LÄS MER