Publications

Click here for a complete CV.

Grant Funding:

  • PI on NSF CAREER Award 2045027, "CAREER: Mean Field Games with Economics Applications: New Techniques in Partial Differential Equations," 8/1/2021 - 7/31/2026

  • co-PI (with Alain Bensoussan, PI) NSF DMS Award 1905449, "New Extensions of the Master Equation in Mean Field Control Theory and Applications," 8/15/2019 - 8/14/2022, $229,999.00 total, $108,999.00 to Baylor.

  • co-PI (with Alain Bensoussan, PI) NSF DMS Award 1612880, "New Problems in Mean Field Control Theory," 9/1/2016 - 8/31/2019, $208,559.00 total, $56,597.00 to Baylor.

Publications:

(with S. Mayorga) "A note on mean field games of controls with state constraints: existence of mild solutions." https://arxiv.org/abs/2109.11655

(with Marcus Laurel) "Parameter sensitivity analysis for mean field games of production." arXiv:2108.10962

(with A. Mullenix and L. Pfeiffer) "Weak Solutions for Potential Mean Field Games of Controls." Nonlinear Differential Equations and Applications Vol. 28, No. 50 (2021). arXiv:2010.09912

(with A. Bensoussan and P. Yam) "Control on Hilbert Space and Application to Mean Field Type Control Theory." arXiv:2005.10770

(with V. Ignazio and A. Neufeld) "Nonlocal Bertrand and Cournot Mean Field Games with General Nonlinear Demand Schedule." Journal de Mathématiques Pures et Appliquées, Volume 148, 2021, Pages 150-198, ISSN 0021-7824. arXiv:2002.11055

(with C. Mouzouni) "On Mean Field Games Models for Exhaustible Commodities Trade," ESAIM:COCV 26 (2020) 11. arxiv:1807.10344

(with A. Meszaros, F. Silva, and D. Tonon) "The planning problem in Mean Field Games as regularized mass transport," Calculus of Variations and PDE (2019) 58: 115. arxiv:1811.02706

(with C. Cotter and R. Kirby) "Mixed finite elements for global tide models with nonlinear damping," Numerische Mathematik, Vol. 140, No. 4 (2018), pp. 963-991. arXiv:1706.01352

(with A. Meszaros) "Sobolev regularity for first order Mean Field Games," Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, Vol. 35, No. 6 (2018), pp. 1557-1576. arXiv:1708.06190

(with C. Mouzouni) "Variational mean field games for market competition," in PDE Models of Multi-Agent Phenomena (2018), vol. 28 of the Springer INdAM Series. arXiv:1707.07853

(with C. Hermosilla and H. Zidani) "Discontinuous solutions of Hamilton-Jacobi equations on networks," Journal of Differential Equations, Vol. 263, No. 12 (2017), pp. 8418 - 8466. hal-01363628

"Linear Quadratic Mean Field Type Control and Mean Field Games with Common Noise, with Application to Production of an Exhaustible Resource," Applied Mathematics and Optimization Vol. 74, No. 3 (special issue, Dec. 2016) pp. 459-486. arXiv:1607.02130

(with A. Bensoussan) "Existence and uniqueness of solutions for Bertrand and Cournot mean field games," Applied Mathematics and Optimization, Vol. 77, No. 1 (2018) pp. 47-71. arXiv:1508.05408

(with J. L. Shomberg) "Attractors for Strongly Damped Wave Equations with Nonlinear Hyperbolic Dynamic Boundary Conditions," Nonlinearity Vol. 29, No. 4, (2016) 1171.

"Weak solutions for mean field games with congestion," preprint.

(with P. Cardaliaguet, A. Porretta, and D. Tonon) "Second order mean field games with degenerate diffusion and local coupling," Nonlinear Differential Equations and Applications (NoDEA), Vol. 22, No. 5 (2015) pp. 1-31.

(with P. Cardaliaguet) "Mean field games systems of first order," ESAIM: Control, Optimization, and Calculus of Variations 21 (2015) 690–722.

"Optimal control of first-order Hamilton-Jacobi equations with linearly bounded Hamiltonians," Applied Mathematics and Optimization, Vol. 70, No. 2 (2014), pp. 185-224, DOI:10.1007/s00245-014-9239-3

(with I. Lasiecka) "Analyticity and Gevrey class regularity for a strongly damped wave equation with hyperbolic dynamic boundary conditions." Semigroup Forum. Vol. 88, No. 2 (2014), pp. 333-365, DOI: 10.1007/s00233-013-9534-3

The Wave Equation with Generalized Nonlinear Acoustic Boundary Conditions. PhD Thesis, University of Virginia, 2012.

(with B. Said-Houari) "Existence and asymptotic behavior of the wave equation with dynamic boundary conditions," Applied Mathematics and Optimization, Vol. 66, No. 1 (2012), pp. 81-122, DOI: 10.1007/s00245-012-9165-1

(with B. Said-Houari) "On the wave equation with semilinear porous acoustic boundary conditions," Journal of Differential Equations, Vol. 252, Issue 9, May 2012, pp. 4898-4941, DOI: 10.1016/j.jde.2012.01.042

"PDE Analysis of Stuctural Acoustic Systems: Well-posedness and Long-time Behavior," 2012 Student Research Conference of the Virginia Space Grant Consortium

"Uniform Boundary Stabilization of a Wave Equation with Nonlinear Acoustic Boundary Conditions and Nonlinear Boundary Damping," Journal of Evolution Equations, Vol. 12, No. 1 (March 2012), pp. 141-164, DOI: 10.1007/s00028-011-0127-x

"Strong Stability and Uniform Decay of Solutions to a Wave Equation with Semilinear Porous Acoustic Boundary Conditions," Nonlinear Analysis: Theory and Applications, Vol. 74, Issue 10, July 2011, pp. 3137-3148, DOI: 10.1016/j.na.2011.01.029

"Wave equation with porous nonlinear acoustic boundary conditions generates a well-posed dynamical system." Nonlinear Analysis: Theory and Applications, Vol. 73, Issue 9, 1 November 2010, pp. 3058-3068, DOI: 10.1016/j.na.2010.06.075

(with E. Abebe and C. Moore.) "Fourier series and the $\delta^2$ process." Journal of Computational and Applied Mathematics. Vol. 224, Issue 1 (Feb. 2009), pp. 146-151, DOI: 10.1016/j.cam.2008.04.020