American Institute of Mathematical Sciences

September  2015, 8(3): 493-531. doi: 10.3934/krm.2015.8.493

Convergence to equilibrium of a linearized quantum Boltzmann equation for bosons at very low temperature

 1 Departamento de Matemáticas, Universidad del País Vasco, (UPV/EHU), Apartado 644, E-48080 Bilbao, Spain 2 Basque Center for Applied Mathematics, Mazarredo 14, E48009 Bilbao, Spain

Received  January 2015 Revised  February 2015 Published  June 2015

We consider an approximation of the linearised equation of the homogeneous Boltzmann equation that describes the distribution of quasiparticles in a dilute gas of bosons at low temperature. The corresponding collision frequency is neither bounded from below nor from above. We prove the existence and uniqueness of solutions satisfying the conservation of energy. We show that these solutions converge to the corresponding stationary state, at an algebraic rate as time tends to infinity.
Citation: Miguel Escobedo, Minh-Binh Tran. Convergence to equilibrium of a linearized quantum Boltzmann equation for bosons at very low temperature. Kinetic & Related Models, 2015, 8 (3) : 493-531. doi: 10.3934/krm.2015.8.493
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