UMA Home page for Philip Jameson Graber
Graber
Philip Jameson
OC team
Former member
was: post-phd
was: post-phd
Ph.D. 2012
EMAIL_TEMPLATE
Research activities
My overall area of research is in nonlinear partial differential equations. I divide my interests into two parts. The first part was the subject of my thesis, the second the subject of my latest post-doctoral research.
- Long-time behavior of nonlinear dissipative PDE systems, with particular applications to acoustic-structure interaction and nonlinear boundary control of wave equations.
- PDE constrained optimization, including problems related to optimal control and Hamilton-Jacobi equations, front propagation, and most recently mean field games.
Here is my CV.
Publications
Papers in peer-reviewed journals
2017
- Discontinuous solutions of Hamilton-Jacobi equations on networks *
, and
Journal of Differential Equations, vol. 263 (12), pp. 8418-8466, Elsevier, 2017
2015
- Mean field games systems of first order
and
ESAIM: Control, Optimisation and Calculus of Variations, vol. 21 (3), pp. 690–722, EDP Sciences, 2015 
2014
- Optimal control of first-order Hamilton-Jacobi equations with linearly bounded Hamiltonian
Applied Mathematics and Optimization, feb, 2014
2013
- Analyticity and Gevrey class regularity for a strongly damped wave equation with hyperbolic dynamic boundary conditions
and
Semigroup Forum, oct, 2013
2012
- Existence and Asymptotic Behavior of the Wave Equation with Dynamic Boundary Conditions
and
Applied Mathematics and Optimization, vol. 66, pp. 81-122, aug, 2012 - On the wave equation with semilinear porous acoustic boundary conditions
and
Journal of Differential Equations, vol. 252, pp. 4898–4941, may, 2012 - Uniform boundary stabilization of a wave equation with nonlinear acoustic boundary conditions and nonlinear boundary damping
Journal of Evolution Equations, vol. 12, pp. 141-164, mar, 2012
2011
- Strong stability and uniform decay of solutions to a wave equation with semilinear porous acoustic boundary conditions
Nonlinear Analysis: Theory, Methods & Applications, vol. 74, pp. 3137-3148, jul, 2011
2010
- Wave equation with porous nonlinear acoustic boundary conditions generates a well-posed dynamical system
Nonlinear Analysis: Theory, Methods and Applications, vol. 73, pp. 3058-3068, nov, 2010
Conferences without proceedings
2014
- Mean field games of first order
and
Southeastern Spring Sectional Meeting of the AMS, mar, 2014 [
]
2013
- Gevrey class regularity for a strongly damped wave equation with hyperbolic dynamic boundary conditions
9th ISAAC congress in Krakow, Poland, aug, 2013 - Optimal control of viscosity solutions to first-order Hamilton-Jacobi equations
Fourth International Conference on Continuous Optimization (ICCOPT); Lisbon, Portugal, 2013
Seminars
2014
- Mean field games and mean field type control: a brief overview
Séminaire Probabilités, Statistiques, Contrôle, mar, 2014 [ ] - Optimal control of Hamilton-Jacobi-Bellman equations
Groupe de Travail Contrôle (Paris 6), jan, 2014 [ ]
2013
- Gevrey class regularity for a strongly damped wave equation with hyperbolic dynamic boundary conditions
and
Groupe de travail : Dynamique globale des systèmes différentiels, may, 2013 [ ]