Upper Maxwellian Bounds for the Spatially Homogeneous Boltzmann Equation

@inproceedings{Gamba2006UpperMB,
  title={Upper Maxwellian Bounds for the Spatially Homogeneous Boltzmann Equation},
  author={Irene M. Gamba and Vladislav A. Panferov and Cristian Villani},
  year={2006}
}
For the spatially homogeneous Boltzmann equation with cutoff hard potentials it is shown that solutions remain bounded from above, uniformly in time, by a Maxwellian distribution, provided the initial data have a Maxwellian upper bound. The main technique is based on a comparison principle that uses a certain dissipative property of the linear Boltzmann equation. Implications of the technique to propagation of upper Maxwellian bounds in the spatially-inhomogeneous case are discussed. 

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References

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Showing 1-10 of 34 references

Moment inequalities for the Boltzmann equation and applications to spatially homogeneous problems

A. V. Bobylev
J. Statist. Phys. 88, • 1997
View 8 Excerpts
Highly Influenced

Some applications of the method of moments for the homogeneous Boltzmann and Kac equations

L. Desvillettes
Arch. Rational Mech. Anal. 123, • 1993
View 5 Excerpts
Highly Influenced

Some relations between nonexpansive and order preserving mappings

M. G. Crandall, L. Tartar
Proc. Amer. Math. Soc. 78, • 1980
View 4 Excerpts
Highly Influenced

Compactness in Boltzmann’s equation via Fourier integral operators and applications

Lions, P.-L
II. J. Math. Kyoto Univ. 34, • 1994
View 7 Excerpts
Highly Influenced

On the Cauchy problem for the Boltzmann equation: Global existence and weak stability

R. DiPerna, Lions, P.-L
Ann. Math • 1989
View 7 Excerpts
Highly Influenced

Global boundedness of moments of solutions of the Boltzmann equation for forces of infinite range

T. Elmroth
Arch. Rational Mech. Anal. 82, • 1983
View 5 Excerpts
Highly Influenced

L∞ estimates for the space-homogeneous Boltzmann equation

L. Arkeryd
J. Statist. Phys. 31, • 1983
View 8 Excerpts
Highly Influenced

The Boltzmann equation. I. Uniqueness and local existence

S. Kaniel, M. Shinbrot
Comm. Math. Phys. 58, • 1978
View 7 Excerpts
Highly Influenced

On the Boltzmann equation. I. Existence II. The full initial value problem

L. Arkeryd
Arch. Rational Mech. Anal • 1972
View 10 Excerpts
Highly Influenced

On the Boltzmann equation in the kinetic theory of gases

A. J. Povzner
Mat. Sb. (N.S.) • 1962
View 4 Excerpts
Highly Influenced

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