A Priori Bounds for Models with Singularities

  • Diogo A. Gomes
  • Edgard A. Pimentel
  • Vardan Voskanyan
Chapter
First Online:
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Abstract

Here, we discuss two problems—an MFG with a logarithmic nonlinearity and an MFG with congestion effects. Stationary versions of these two problems were considered in Chap.  7 However, the techniques for time-dependent problems are substantially different from the ones used in the stationary case.

This is a preview of subscription content, log in to check access.

References

  1. 114.
    D. Gomes, H. Mitake, Existence for stationary mean-field games with congestion and quadratic Hamiltonians. Nonlinear Differ. Equ. Appl. 22 (6), 1897–1910 (2015)MathSciNetCrossRefMATHGoogle Scholar
  2. 117.
    D. Gomes, E. Pimentel, Time dependent mean-field games with logarithmic nonlinearities. SIAM J. Math. Anal. 47 (5), 3798–3812 (2015)MathSciNetCrossRefMATHGoogle Scholar
  3. 123.
    D. Gomes, V. Voskanyan, Short-time existence of solutions for mean-field games with congestion. J. Lond. Math. Soc. (2) 92 (3), 778–799 (2015)Google Scholar
  4. 136.
    J. Graber, Weak solutions for mean field games with congestion. Preprint (2015)Google Scholar
  5. 174.
    P.-L. Lions, Collège de France course on Mean-Field Games. 2007–2011Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Diogo A. Gomes
    • 1
  • Edgard A. Pimentel
    • 2
  • Vardan Voskanyan
    • 1
  1. 1.CEMSE DivisionKing Abdullah University of Science and TechnologyThuwalSaudi Arabia
  2. 2.Department of MathematicsUniversidade Federal de Sao CarlosSão CarlosBrazil

Personalised recommendations