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On Exponential‐Asymptotic Stability Properties of B OLTZMANN 's Equation and a Class of its Modifications
Author(s) -
Maass W.
Publication year - 1972
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19724830303
Subject(s) - exponential stability , class (philosophy) , exponential function , stability (learning theory) , mathematical analysis , physics , boundary (topology) , mathematics , nonlinear system , quantum mechanics , computer science , artificial intelligence , machine learning
For the linearized B OLTZMANN equation and a class of “modifications” of the linearized B OLTZMANN equation (including the usual B OLTZMANN equation) exponential‐asymptotic stability of the total equilibrium is proved with respect to some boundary and existence assumptions which seem to be physically reasonable. Of course, this structural stability is important if B OLTZMANN 's equation has to be considered under the influence of “perturbations” or if it is substituted by model equations.