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A note on the solvability of Boltzmann's equation via comparison methods
Author(s) -
Wieser W.,
Neunzert H.
Publication year - 1985
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670070122
Subject(s) - mathematics , boltzmann equation , contraction (grammar) , argument (complex analysis) , space (punctuation) , section (typography) , boltzmann constant , interval (graph theory) , mathematical analysis , calculus (dental) , combinatorics , computer science , medicine , biochemistry , chemistry , physics , dentistry , quantum mechanics , thermodynamics , operating system
We consider the Cauchyproblem for the space‐inhomogeneous Boltzmann equation. For the so‐called soft‐interaction case we prove unique local solvability, analogous to a result of Palczewski [1]. However, since in our proof a comparison argument is used rather than the familiar contraction mapping principle, we are able to extend the previously known time‐interval of existence. In a final section the two main difficulties in generalizing the result are discussed in some detail.