Properties of stationary solutions of a generalized Tjon-Wu equation |
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| Authors: | Andrzej Lasota |
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| Institution: | a Institute of Mathematics, Silesian University, and Institute of Mathematics, Polish Academy of Sciences, Bankowa 14, 40-007 Katowice, Poland
b Institute of Computer Sciences, Jagiellonian University, Nawojki 11, 30-072 Kraków, Poland |
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| Abstract: | A generalized version of the Tjon-Wu equation is considered. Solutions of this equation are functions with values in the space of probability measures on 0,∞). We prove that the stationary solution μ∗ of the equation has the following property: Either μ∗ is supported at one point or suppμ∗=0,∞). Moreover we show that in the second case the distribution function of μ∗ is continuous. Some open questions are discussed. |
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| Keywords: | Tjon-Wu equation Invariant measure Boltzmann equation |
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