INTERPLAY OF ELASTIC AND INELASTIC SCATTERING OPERATORS IN EXTENDED KINETIC MODELS AND THEIR HYDRODYNAMIC LIMITS: REFERENCE MANUAL

REFERENCES

• Banasiak , J. 2000 . Mathematical Properties of Inelastic Scattering Models in Linear Kinetic Theory . Math. Mod. Meth. Appl. Sci. , 10 ( 2 ) : 163 – 186 .
   Web of Science ®Google Scholar
• Banasiak , J. 2000 . Diffusion Approximation of an Inelastic Scattering Model in Linear Kinetic Theory . Adv. Math. Sci. Appl. , 10 ( 1 ) : 375 – 397 .
   Google Scholar
• Banasiak , J. 2000 . On a Diffusion-Kinetic Equation Arising in Extended Kinetic Theory . Math. Methods Appl. Sci. , 23 ( 14 ) : 1237 – 1256 .
   Google Scholar
• Banasiak , J. 2000 . The Existence of Moments of Solutions to Transport Equations with Inelastic Scattering and Their Application in the Asymptotic Analysis . J. Appl. Analysis , 6 ( 2 ) : 13 – 32 .
   Google Scholar
• Banasiak , J. 2001 . On the Hydrodynamic Limit of a Linear Kinetic Equation with Dominant Elastic Scattering . Atti. Sem. Mat. Fis. Univ. Modena , IL ( 1 ) : 221 – 245 .
   Google Scholar
• Banasiak , J. and Demeio , L. 1999 . Diffusion Approximations of a Linear Kinetic Equation with Inelastic Scattering: Asymptotic Analysis and Numerical Results . Transport Theory Stat. Phys. , 28 ( 5 ) : 475 – 498 .
   Web of Science ®Google Scholar
• Banasiak , J. , Frosali , G. and Spiga , G. 1998 . Asymptotic Analysis for a Particle Transport Equation with Inelastic Scattering in Extended Kinetic Theory . Math. Mod. Meth. Appl. Sci. , 8 ( 5 ) : 851 – 874 .
   Web of Science ®Google Scholar
• Banasiak , J. , Frosali , G. and Spiga , G. 2000 . Inelastic Scattering Models in Transport Theory and Their Small Mean Free Path Analysis . Math. Meth. Appl. Sci. , 23 : 121 – 145 .
   Web of Science ®Google Scholar
• Belleni-Morante , A. and McBride , A.C. 1998 . Applied Nonlinear Semigroups Chichester : J. Wiley .
   Google Scholar
• Ben Abdallah , N. and Degond , P. 1996 . On Hierarchy of Macroscopic Models for Semiconductors . J. Math. Phys. , 37 ( 7 ) : 3306 – 3333 .
   Google Scholar
• Bobylev , A.V. and Spiga , G. 1998 . On a Model Transport Equation with Inelastic Scattering . SIAM J. Appl. Math. , 58 : 1128 – 1137 .
   Google Scholar
• Caraffini , G.L. , Catalano , C.E. and Spiga , G. 1998 . On the Small Mean Free Path Asymptotics of the Transport Equation with Inelastic Scattering . Riv. Mat. Univ. Parma, Serie VI , 1 : 13 – 30 .
   Google Scholar
• Case , K.M. and Zweifel , P.F. 1967 . Linear Transport Theory Reading : Addison-Wesley .
   Google Scholar
• Cercignani , C. 1988 . The Boltzmann Equation and Its Applications New York : Springer Verlag .
   Google Scholar
• Cercignani , C. and Sattinger , D. 1998 . Scaling Limits and Models in Physical Processes Basel : Birkhäuser .
   Google Scholar
• Demeio , L. and Frosali , G. 1998 . Diffusion Approximations of Kinetic Equations with Elastic and Inelastic Scattering: a Comparison of Different Scalings . Sommari del IV Congresso Naz. Soc. Ital. di Matematica Industriale e Applicata SIMAI98 . 1998 . Vol. 2 , pp. 316 – 319 . Giardini Naxos (Messina), 1-5 giugno
   Google Scholar
• Demeio , L. and Frosali , G. 1999 . Different Scalings in the Asymptotic Analysis of Kinetic Equations with Elastic and Inelastic Scattering Università di Ancona, Dipartimento di Matematica . Rapporto N.2—Aprile
   Google Scholar
• Eliason , M.A. and Hirschfelder , J.O. 1959 . General Collision Theory Treatment for the Rate of Bimolecular Gas Phase Reactions . J. Chem. Phys. , 30 : 1426 – 1436 .
   Web of Science ®Google Scholar
• Engel , K.-J. and Nagel , R. 1999 . One-parameter Semigroups for Linear Evolution Equations, Graduate Texts in Mathematics Wien : Springer Verlag .
   Google Scholar
• Ferziger , J.H. and Kaper , H.G. 1972 . Mathematical Theory of Transport Processes in Gases Amsterdam, , North Holland
   Google Scholar
• Frosali , G. 1998 . Asymptotic Analysis for a Particle Transport Problem in a Moving Medium . IMA J. Appl. Math. , 60 : 167 – 185 .
   Google Scholar
• Garibotti , C.R. and Spiga , G. 1994 . Boltzmann Equation for Inelastic Scattering . J. Phys. A: Math. Gen. , 27 : 2709 – 2717 .
   Google Scholar
• Grad , H. 1963 . Asymptotic Theory of the Boltzmann Equation . Physics of Fluids , 6 ( 2 ) : 147 – 181 .
   Google Scholar
• Groppi , M. and Spiga , G. 1999 . Kinetic Approach to Chemical Reactions and Inelastic Transitions in a Rarefied Gas . J. Math. Chem. , 26 : 197 – 219 .
   Web of Science ®Google Scholar
• Henry , D. 1981 . Geometric Theory of Semilinear Equations New York : Springer Verlag . LNM 840
   Google Scholar
• Hilbert , D. 1912 . Begründung der kinetischen Gastheorie . Math. Ann. , 72 : 562 – 577 .
   Google Scholar
• Light , J.C. , Ross , J. and Shuler , K.E. 1969 . “ Rate Coefficients, Reaction Cross Sections, and Microscopic Reversibility ” . In Kinetic Processes in Gases and Plasmas Edited by: Hochstim , A.R. New York : Academic Press .
   Google Scholar
• Majorana , A. 1991 . Space Homogeneous Solutions of the Boltzmann Equation Describing Electron–Phonon Interaction in Semiconductors . Transport Theory Stat. Phys. , 20 ( 4 ) : 261 – 279 .
   Google Scholar
• Markowich , P.A. , Ringhofer , Ch.A. and Schmeiser , Ch. 1990 . Semiconductor Equations Wien : Springer Verlag .
   Google Scholar
• Markowich , P.A. and Schmeiser , Ch. 1997 . The Drift-Diffusion Limit for Electron-Phonon Interaction in Semiconductors . Math. Mod. Meth. Appl. Sci. , 7 ( 5 ) : 707 – 729 .
   Google Scholar
• Mika , J.R. and Banasiak , J. 1995 . Singularly Perturbed Evolution Equations with Applications in Kinetic Theory Singapore : World Scientific .
   Google Scholar
• Mika , J.R. 1981 . New Asymptotic Expansion Algorithm for Singularly Perturbed Evolution Equations . Math. Methods Appl. Sci. , 3 : 172 – 188 .
   Google Scholar
• Mokhtar-Kharroubi , M. 1997 . Mathematical Topics in Neutron Theory: New Aspects Singapore : World Scientific .
   Google Scholar
• Rossani , A. and Spiga , G. 1998 . Kinetic Theory with Inelastic Interactions . Transport Theory Stat. Phys. , 27 : 273 – 287 .
   Google Scholar
• Rossani , A. and Spiga , G. 1999 . A Note on the Kinetic Theory of Chemically Reacting Gases . Physica A , 272 : 563 – 573 .
   Web of Science ®Google Scholar
• Truesdell , C. and Muncaster , R.G. 1980 . Fundamentals of Maxwell's Kinetic Theory of a Simple Monoatomic Gas New York : Academic Press .
   Google Scholar
• Wang Chang , C.S. , Uhlenbeck , G.E. and De Boer , J. 1969 . “ The Heat Conductivity and Viscosity of Polyatomic Gases ” . In Studies in Statistical Mechanics Edited by: De Boer , J. Vol. 2 , Amsterdam, , North Holland
   Google Scholar