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Volumn 10, Issue 1, 2017, Pages 117-140

Balanced growth path solutions of a Boltzmann mean field game model for knowledge growth

Author keywords

Boltzmann type equations; Hamilton Jacobi equations; Mean field games; Travelling wave solutions

Indexed keywords


EID: 85010206619     PISSN: 19375093     EISSN: 19375077     Source Type: Journal    
DOI: 10.3934/krm.2017005     Document Type: Article
Times cited : (21)

References (24)
  • 1
    • 84907863441 scopus 로고    scopus 로고
    • Partial differential equation models in macroeconomics, Philosophical Transactions of the Royal Society of London A: Mathematical
    • Y. Achdou, F. J. Buera, J.-M. Lasry, P.-L. Lions and B. Moll, Partial differential equation models in macroeconomics, Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 372 (2014), 20130397, 19 pp.
    • (2014) Physical and Engineering Sciences , vol.372 , pp. 19
    • Achdou, Y.1    Buera, F.J.2    Lasry, J.-M.3    Lions, P.-L.4    Moll, B.5
  • 3
    • 0000229982 scopus 로고
    • Weitere Studien über das Wärmegleichgewicht unter Gasmolekulen
    • L. Boltzmann, Weitere Studien über das Wärmegleichgewicht unter Gasmolekulen, Wien. Ber, 66 (1872), 275-370.
    • (1872) Wien. Ber , vol.66 , pp. 275-370
    • Boltzmann, L.1
  • 4
    • 67650100840 scopus 로고    scopus 로고
    • A kinetic approach to the study of opinion formation
    • L. Boudin and F. Salvarani, A kinetic approach to the study of opinion formation, M2AN Math. Model. Numer. Anal., 43 (2009), 507-522, URL http://dx.doi.org/10.1051/m2an/2009004.
    • (2009) M2AN Math. Model. Numer. Anal , vol.43 , pp. 507-522
    • Boudin, L.1    Salvarani, F.2
  • 6
    • 84992670197 scopus 로고    scopus 로고
    • On a Boltzmann mean field model for knowledge growth
    • arXiv preprint arXiv:1503.08419
    • M. Burger, A. Lorz and M.-T. Wolfram, On a Boltzmann mean field model for knowledge growth, SIAM J. Appl. Math., 76 (2016), 1799-1818, arXiv preprint arXiv:1503.08419.
    • (2016) SIAM J. Appl. Math , vol.76 , pp. 1799-1818
    • Burger, M.1    Lorz, A.2    Wolfram, M.-T.3
  • 8
    • 84898548072 scopus 로고    scopus 로고
    • Large-scale dynamics of mean-field games driven by local Nash equilibria
    • P. Degond, J.-G. Liu and C. Ringhofer, Large-scale dynamics of mean-field games driven by local Nash equilibria, Journal of Nonlinear Science, 24 (2014), 93-115.
    • (2014) Journal of Nonlinear Science , vol.24 , pp. 93-115
    • Degond, P.1    Liu, J.-G.2    Ringhofer, C.3
  • 9
    • 0001089576 scopus 로고
    • On the Cauchy problem for Boltzmann equations: Global existence and weak stability
    • R. J. DiPerna and P.-L. Lions, On the Cauchy problem for Boltzmann equations: Global existence and weak stability, Annals of Mathematics, 130 (1989), 321-366.
    • (1989) Annals of Mathematics , vol.130 , pp. 321-366
    • DiPerna, R.J.1    Lions, P.-L.2
  • 11
    • 56649120231 scopus 로고    scopus 로고
    • Kinetic equations modelling wealth redistribution: A comparison of approaches
    • B. Düring, D. Matthes and G. Toscani, Kinetic equations modelling wealth redistribution: A comparison of approaches, Physical Review E, 78 (2008), 056103, 12pp.
    • (2008) Physical Review E , vol.78 , pp. 12
    • Düring, B.1    Matthes, D.2    Toscani, G.3
  • 12
    • 84964692616 scopus 로고    scopus 로고
    • Diffusive and inviscid traveling waves of the Fisher equation and nonuniqueness of wave speed
    • D. Hilhorst and Y.-J. Kim, Diffusive and inviscid traveling waves of the Fisher equation and nonuniqueness of wave speed, Applied Mathematics Letters, 60 (2016), 28-35.
    • (2016) Applied Mathematics Letters , vol.60 , pp. 28-35
    • Hilhorst, D.1    Kim, Y.-J.2
  • 14
    • 58149123453 scopus 로고    scopus 로고
    • Ideas and growth
    • R. E. Lucas, Ideas and growth, Economica, 76 (2009), 1-19, URL http://dx.doi.org/10. 1111/j.1468-0335.2008.00748.x.
    • (2009) Economica , vol.76 , pp. 1-19
    • Lucas, R.E.1
  • 16
    • 85010189775 scopus 로고    scopus 로고
    • Noise and Imitation Implies Balanced Growth, Technical report, Federal Reserve Bank of Minneapolis
    • E. G. Luttmer, Eventually, Noise and Imitation Implies Balanced Growth, Technical report, Federal Reserve Bank of Minneapolis, 2012.
    • (2012) Eventually
    • Luttmer, E.G.1
  • 19
    • 0019589720 scopus 로고
    • Mathematical model for the diffusion of innovation
    • P. Markowich, Mathematical model for the diffusion of innovation, IEEE Trans. Sys., Man, and Cyber., 11 (1981), 504-509.
    • (1981) IEEE Trans. Sys., Man, and Cyber , vol.11 , pp. 504-509
    • Markowich, P.1
  • 20
    • 84907865727 scopus 로고    scopus 로고
    • Wealth distribution and collective knowledge: A Boltzmann approach, Philosophical Transactions of the Royal Society A: Mathematical
    • L. Pareschi and G. Toscani, Wealth distribution and collective knowledge: A Boltzmann approach, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engi-neering Sciences, 372 (2014), 20130396, 15 pp, URL http://rsta.royalsocietypublishing. org/content/372/2028/20130396.abstract.
    • (2014) Physical and Engi-neering Sciences , vol.372 , pp. 15
    • Pareschi, L.1    Toscani, G.2
  • 22
    • 83055172970 scopus 로고    scopus 로고
    • Growth and the diffusion of ideas
    • M. Staley, Growth and the diffusion of ideas, Journal of Mathematical Economics, 47 (2011), 470-478.
    • (2011) Journal of Mathematical Economics , vol.47 , pp. 470-478
    • Staley, M.1
  • 24
    • 67649344144 scopus 로고    scopus 로고
    • A review of mathematical topics in collisional kinetic theory
    • C. Villani, A review of mathematical topics in collisional kinetic theory, Handbook of Math-ematical Fluid Dynamics, 1 (2002), 71-305.
    • (2002) Handbook of Math-ematical Fluid Dynamics , vol.1 , pp. 71-305
    • Villani, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.