The positivity principle in Boltzmann-type equations
Abstract
Classical theorems about matrices with non-negative elements can be generalized for application in eigenvalue problems of integrodifferential form appearing in the description of stationary particle transport. The existence and unicity of positive L(1)-eigensolutions of the m-quasi-completely-continuous transport operator can be deduced. These solutions can be realized by a method of successive approximation.
- Publication:
-
Mathematical Methods in the Applied Sciences
- Pub Date:
- 1980
- DOI:
- 10.1002/mma.1670020407
- Bibcode:
- 1980MMAS....2..445E
- Keywords:
-
- Boltzmann Transport Equation;
- Eigenvalues;
- Integral Equations;
- Particle Motion;
- Statistical Mechanics;
- Existence Theorems;
- Iterative Solution;
- Operators (Mathematics);
- Uniqueness Theorem;
- Thermodynamics and Statistical Physics