Asymptotic Analysis of a Non-Linear Non-Local Integro-Differential Equation Arising from Bosonic Quantum Field Dynamics

Sébastien Breteaux (1)

1 IAA - Institut for Analysis and Algebra

We introduce a one parameter family of non-linear, non-local integro-differential equations and its limit equation. These equations originate from a derivation of the linear Boltzmann equation using the framework of bosonic quantum field theory. We show the existence and uniqueness of strong global solutions for these equations, and a result of uniform convergence on every compact interval of the solutions of the one parameter family towards the solution of the limit equation.

Mots clés: integro-differential equation; nonlinear equation; nonlocal equation; equation with memory

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Sébastien Breteaux. Asymptotic Analysis of a Non-Linear Non-Local Integro-Differential Equation Arising from Bosonic Quantum Field Dynamics. Nonlinear Differential Equations and Applications, 2014, 21 (1), pp.51-61. ⟨10.1007/s00030-013-0237-y⟩. ⟨hal-00767171⟩