The Cauchy problem for the generalized Boltzmann equation with dissipative collisions

Applied Mathematics Letters

Volumn 14, Issue 8, 2001, Pages 941-947

  De Angelis, E ^a   Grunfeld C P ^b  

^a POLITECNICO DI TORINO   (Italy)

^b INSTITUTE OF SPACE SCIENCES   (Romania)

Author keywords

Boltzmann equation; Cauchy problem; Dissipative collisions; Generalized Boltzmann models

Indexed keywords

EID: 0035501706     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-9659(01)00069-6     Document Type: Article

References (10)

1. Esteban M., Perthame B. On the modified Enskog equation for elastic and inelastic collisions. Models with Spin. Ann. Inst. Poincare. 8:1991;289-308.
2. DiPerna R., Lions P.L. On the Cauchy problem for the Boltzmann equation: Global existence and weak stability results. Annals Math. 130:1989;321-366.
3. Bellomo N., Esteban M., Lachowicz M. Nonlinear kinetic equations with dissipative collisions. Appl. Math. Lett. 8:(5):1995;47-52.
4. Bellomo N., Polewczak J. The generalized Boltzmann equation. Solution and exponential trend to equilibrium. Transp. Theory Stat. Phys. 26:1997;661-677.
5. Glassey R.T. The Cauchy Problem in Kinetic Theory. 1996;SIAM, Philadelphia, PA.
6. Bellomo N., Pulvirenti M. Modelling in Applied Sciences: A Kinetic Theory Approach. 1999;Birkhäuser, Boston, MA.
7. Bobilev A.V., Carrillo J.A., Gamba I.M. On some properties of kinetic and hydrodynamic equations for inelastic interactions. J. Stat. Phys. 98:2000;743-773.
8. Arkeryd L. On the Boltzmann Equation I & II. Arch. Rat. Mech. Anal. 45:1972;1-34.
9. Povzner A.Ya. About the Boltzmann equation in kinetic theory of gases. Mat. Sborn. 58:1962;65-86.
10. Schaefer H.H. Banach Lattices and Positive Operators. 1974;Springer, Berlin.