Methods and Applications of Analysis
Volume 14 (2007)
Asymptotic Completeness for Relativistic Kinetic Equations with Short-range Interaction Forces
Pages: 251 – 262
We present an $L^1$-asymptotic completeness results for relativistic kinetic equations with short range interaction forces. We show that the uniform phase space-time bound for nonlinear terms to the relativistic nonlinear kinetic equations yields the asymptotic completeness of the relativistic kinetic equations. For this space-time bound, we employ dispersive estimates and explicit construction of a Lyapunov functional.
Asymptotic completeness; relativistic kinetic equation; the Vlasov-Yukawa equation; the Klein-Gordon equation
2010 Mathematics Subject Classification
Primary 35L45. Secondary 70K20, 70K40.