## On the stationary Povzner equation in $$\mathbb R^n$$.(English)Zbl 1010.35022

The authors investigate the stationary Povzner equation (a Boltzmann-type kinetic equation with a mollification in space of the collision terms) in a bounded and strictly convex domain $$\Omega$$ of $$\mathbb R^n.$$ Boundary conditions of diffusive reflection and collision kernels including hard forces are permitted. Skillful approximations plus compactness methods such as velocity averaging and use of the entropy dissipation are employed to prove the existence of weak solutions.

### MSC:

 35D05 Existence of generalized solutions of PDE (MSC2000) 76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics 35Q35 PDEs in connection with fluid mechanics 82C40 Kinetic theory of gases in time-dependent statistical mechanics
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