# The Boltzmann Equation: Mathematics and Applications

Bollettino dell'Unione Matematica Italiana (2007)

- Volume: 10-B, Issue: 2, page 293-315
- ISSN: 0392-4041

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topCercignani, Carlo. "The Boltzmann Equation: Mathematics and Applications." Bollettino dell'Unione Matematica Italiana 10-B.2 (2007): 293-315. <http://eudml.org/doc/290450>.

@article{Cercignani2007,

abstract = {The paper is subdivided into two parts. The first presents a recent result by the author concerning the existence of the solution of the Boltzmann equation for Maxwell molecules, without any cutoff in the collision kernel, when the solution depends on just one variable. At variance with the well-known theorem of DiPerna- Lions, conservation of energy is also shown to hold. The second part will concern rarefied gas dynamics problems, governed by the Boltzmann equation and con- cerning the theory of micromachines (MEMS) and nanomachines (NENS).},

author = {Cercignani, Carlo},

journal = {Bollettino dell'Unione Matematica Italiana},

language = {eng},

month = {6},

number = {2},

pages = {293-315},

publisher = {Unione Matematica Italiana},

title = {The Boltzmann Equation: Mathematics and Applications},

url = {http://eudml.org/doc/290450},

volume = {10-B},

year = {2007},

}

TY - JOUR

AU - Cercignani, Carlo

TI - The Boltzmann Equation: Mathematics and Applications

JO - Bollettino dell'Unione Matematica Italiana

DA - 2007/6//

PB - Unione Matematica Italiana

VL - 10-B

IS - 2

SP - 293

EP - 315

AB - The paper is subdivided into two parts. The first presents a recent result by the author concerning the existence of the solution of the Boltzmann equation for Maxwell molecules, without any cutoff in the collision kernel, when the solution depends on just one variable. At variance with the well-known theorem of DiPerna- Lions, conservation of energy is also shown to hold. The second part will concern rarefied gas dynamics problems, governed by the Boltzmann equation and con- cerning the theory of micromachines (MEMS) and nanomachines (NENS).

LA - eng

UR - http://eudml.org/doc/290450

ER -

## References

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