Verfügbarkeit: The mathematical theory of dilute gases

The mathematical theory of dilute gases:

Gespeichert in:

Bibliographische Detailangaben
Beteiligte Personen:	Cercignani, Carlo 1939-2010 (VerfasserIn), Illner, Reinhard 1950- (VerfasserIn), Pulvirenti, Mario (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	New York [u.a.] Springer 1994
Schriftenreihe:	Applied mathematical sciences 106
Schlagwörter:	Mathematische Physik Chemistry, Physical and theoretical Kinetic theory of gases Mathematical physics Transport theory Boltzmann-Gleichung Kinetische Gastheorie Mathematisches Modell Verdünntes Gas Transporttheorie
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006417405&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	VII, 347 S. graph. Darst.
ISBN:	0387942947 3540942947

Internformat

MARC


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Datensatz im Suchindex

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adam_text	CARLO CERCIGNANI REINHARD ILLNER MARIO PULVIRENTI THE MATHEMATICAL THEORY OF DILUTE GASES WITH 34 ILLUSTRATIONS SPRINGER-VERLAG NEW YORK BERLIN HEIDELBER G LONDO N PARI S TOKY O HON G KONG BARCELON A BUDAPES T CONTENT S INTRODUCTIO N .. . 1 1 HISTORICA L INTRODUCTIO N .. . 4 1.1 WHA T IS A GAS? FRO M TH E BILLIARD TABL E T O BOYLE S LAW .. . 4 1.2 BRIEF HISTOR Y OF KINETI C THEOR Y .. . 8 2 INFORMAL DERIVATIO N OF TH E BOLTZMAN N EQUATIO N .. . 13 2.1 TH E PHAS E SPACE AN D TH E LIOUVILLE EQUATIO N .. . 13 2.2 BOLTZMANN S ARGUMEN T I N A MODER N PERSPECTIV E .. . 19 2.3 MOLECULAR CHAOS . CRITIQU E AN D JUSTIFICATIO N .. . 24 2.4 TH E BBGK Y HIERARCHY .. . 26 2.5 TH E BOLTZMAN N HIERARCHY AN D IT S RELATIO N T O TH E BOLTZMAN N EQUATIO N .. . 29 3 ELEMENTAR Y PROPERTIE S OF TH E SOLUTION S .. . 33 3.1 COLLISION INVARIANT S .. . 3 3 3.2 TH E BOLTZMAN N INEQUALIT Y AN D TH E MAXWELL DISTRIBUTION S . . .42 3.3 TH E MACROSCOPIC BALANC E EQUATION S .. . 4 3 3.4 TH E H-THEORE M .. . 49 3.5 LOSCHMIDT S PARADO X .. . 52 3.6 POINCARE S RECURRENC E AN D ZERMELO S PARADO X .. . 55 3.7 EQUILIBRIU M STATE S AN D MAXWELLIAN DISTRIBUTION S .. . 56 3.8 HYDRODYNAMICA L LIMIT AN D OTHE R SCALINGS .. . 57 4 RIGOROUS VALIDITY OF TH E BOLTZMAN N EQUATIO N .. . 63 4.1 SIGNIFICANCE OF TH E PROBLE M .. . 63 VI CONTENTS 4.2 HARD-SPHER E DYNAMICS .. . 64 4.3 TRANSITIO N T O L 1 . TH E LIOUVILLE EQUATIO N AN D TH E BBGK Y HIERARCHY REVISITED .. . 68 4.4 RIGOROUS VALIDITY OF TH E BOLTZMAN N EQUATIO N .. . 72 4.5 VALIDITY OF TH E BOLTZMAN N EQUATIO N FOR A RAR E CLOUD OF GA S IN TH E VACUUM .. . 87 4.6 INTERPRETATIO N .. . 90 4.7 TH E EMERGENCE OF IRREVERSIBILITY .. . 95 4.8 MORE ON TH E BOLTZMAN N HIERARCH Y .. . 100 APPENDI X 4.A MORE ABOU T HARD-SPHER E DYNAMIC S .. . 107 APPENDI X 4.YY A RIGOROUS DERIVATIO N OF TH E BBGK Y HIERARCHY .. . 115 APPENDI X 4.YY UCHIYAMA S EXAMPL E .. . 123 EXISTENC E AN D UNIQUENESS RESULT S .. . 133 5.1 PRELIMINAR Y REMARK S .. . 133 5.2 EXISTENC E FROM VALIDITY, AN D OVERVIEW .. . 135 5.3 A GENERA L GLOBAL EXISTENC E RESUL T .. . 139 5.4 GENERALIZATION S AN D OTHE R REMARK S .. . 161 APPENDI X 5.A .. . 164 TH E INITIA L VALUE PROBLE M FOR TH E HOMOGENEOUS BOLTZMAN N EQUATIO N .. . 167 6.1 A N EXISTENC E THEORE M FOR A MODIFIED EQUATIO N .. . 167 6.2 REMOVING TH E CUTOFF: TH E Z^-THEOR Y FOR TH E FULL EQUATIO N .. . 171 6.3 TH E L-THEOR Y AN D CLASSICAL SOLUTION S .. . 177 6.4 LONG TIM E BEHAVIOR .. . 182 6.5 FURTHE R DEVELOPMENTS AN D COMMENT S .. . 183 APPENDI X 6.A .. . 186 APPENDI X 6.B .. . 188 APPENDI X 6.C .. . 189 PERTURBATION S OF EQUILIBRI A AN D SPACE HOMOGENEOUS SOLUTIONS . . .191 7.1 TH E LINEARIZED COLLISION OPERATO R .. . 191 7.2 TH E BASIC PROPERTIE S OF TH E LINEARIZED COLLISION OPERATO R .. . 194 7.3 SPECTRA L PROPERTIE S OF TH E FOURIER-TRANSFORMED, LINEARIZED BOLTZMAN N EQUATIO N .. . 202 7.4 TH E ASYMPTOTI C BEHAVIOR OF TH E SOLUTION OF TH E CAUCHY PROBLE M FOR TH E LINEARIZED BOLTZMAN N EQUATIO N .. . 213 7.5 TH E GLOBAL EXISTENC E THEORE M FOR TH E NONLINEAR EQUATIO N . . .217 7.6 EXTENSIONS : TH E PERIODI C CASE AN D PROBLEM S IN ON E AN D TWO DIMENSIONS .. . 219 7.7 A FURTHE R EXTENSION : SOLUTIONS CLOSE T O A SPACE HOMOGENEOUS SOLUTION .. . 221 CONTENTS VII 8 BOUNDAR Y CONDITION S .. . 226 8.1 INTRODUCTIO N .. . 226 8.2 TH E SCATTERIN G KERNE L .. . 227 8.3 TH E ACCOMMODATIO N COEFFICIENTS .. . 231 8.4 MATHEMATICA L MODELS .. . 235 8.5 A REMARKABL E INEQUALIT Y .. . 239 9 EXISTENC E RESULT S FOR INITIAL-BOUNDAR Y AN D BOUNDAR Y VALUE PROBLEM S .. . 244 9.1 PRELIMINAR Y REMARK S .. . 244 9.2 RESULT S ON TH E TRACE S .. . 246 9.3 PROPERTIE S OF TH E FREE-STREAMIN G OPERATO R .. . 254 9.4 EXISTENC E IN A VESSEL WIT H ISOTHERMA L BOUNDAR Y .. . 259 9.5 RIGOROUS PROOF OF TH E APPROAC H T O EQUILIBRIU M .. . 267 9.6 PERTURBATION S OF EQUILIBRI A .. . 271 9.7 A STEAD Y PROBLE M .. . 273 9.8 STABILIT Y OF TH E STEAD Y FLOW PAS T A N OBSTACL E .. . 281 9.9 CONCLUDIN G REMARK S .. . 283 10 PARTICL E SIMULATIO N OF TH E BOLTZMAN N EQUATIO N .. . 286 10.1 RATIONAL E AM D OVERVIEW .. . 286 10.2 LOW DISCREPANC Y METHOD S .. . 289 10.3 BIRD S SCHEME .. . 303 11 HYDRODYNAMICA L LIMIT S .. . 312 11.1 A FORMA L DISCUSSION .. . 312 11.2 TH E HILBER T EXPANSIO N .. . 316 11.3 TH E ENTROP Y APPROAC H T O TH E HYDRODYNAMICA L LIMIT .. . 318 11.4 TH E HYDRODYNAMICA L LIMIT FOR SHOR T TIME S .. . 322 11.5 OTHE R SCALINGS AN D TH E INCOMPRESSIBLE NAVIER-STOKES EQUATION S .. . 330 12 OPE N PROBLEM S AN D NEW DIRECTION S .. . 336 AUTHO R INDE X .. . 342 SUBJEC T INDE X .. . 345
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series	Applied mathematical sciences
series2	Applied mathematical sciences
spellingShingle	Cercignani, Carlo 1939-2010 Illner, Reinhard 1950- Pulvirenti, Mario The mathematical theory of dilute gases Applied mathematical sciences Mathematische Physik Chemistry, Physical and theoretical Kinetic theory of gases Mathematical physics Transport theory Boltzmann-Gleichung (DE-588)4146261-0 gnd Kinetische Gastheorie (DE-588)4163881-5 gnd Mathematisches Modell (DE-588)4114528-8 gnd Verdünntes Gas (DE-588)4300367-9 gnd Transporttheorie (DE-588)4185936-4 gnd Mathematische Physik (DE-588)4037952-8 gnd
subject_GND	(DE-588)4146261-0 (DE-588)4163881-5 (DE-588)4114528-8 (DE-588)4300367-9 (DE-588)4185936-4 (DE-588)4037952-8
title	The mathematical theory of dilute gases
title_auth	The mathematical theory of dilute gases
title_exact_search	The mathematical theory of dilute gases
title_full	The mathematical theory of dilute gases Carlo Cercignani ; Reinhard Illner ; Mario Pulvirenti
title_fullStr	The mathematical theory of dilute gases Carlo Cercignani ; Reinhard Illner ; Mario Pulvirenti
title_full_unstemmed	The mathematical theory of dilute gases Carlo Cercignani ; Reinhard Illner ; Mario Pulvirenti
title_short	The mathematical theory of dilute gases
title_sort	the mathematical theory of dilute gases
topic	Mathematische Physik Chemistry, Physical and theoretical Kinetic theory of gases Mathematical physics Transport theory Boltzmann-Gleichung (DE-588)4146261-0 gnd Kinetische Gastheorie (DE-588)4163881-5 gnd Mathematisches Modell (DE-588)4114528-8 gnd Verdünntes Gas (DE-588)4300367-9 gnd Transporttheorie (DE-588)4185936-4 gnd Mathematische Physik (DE-588)4037952-8 gnd
topic_facet	Mathematische Physik Chemistry, Physical and theoretical Kinetic theory of gases Mathematical physics Transport theory Boltzmann-Gleichung Kinetische Gastheorie Mathematisches Modell Verdünntes Gas Transporttheorie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006417405&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000005274
work_keys_str_mv	AT cercignanicarlo themathematicaltheoryofdilutegases AT illnerreinhard themathematicaltheoryofdilutegases AT pulvirentimario themathematicaltheoryofdilutegases

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