Tien Khai Nguyen

GENERIC PROPERTIES OF CONJUGATE POINTS IN OPTIMAL CONTROL PROBLEMS

Bressan, A., Mazzola, M., & Nguyen, K. t. (2024, September). MATHEMATICAL CONTROL AND RELATED FIELDS.

Piecewise regular solutions to scalar balance laws with singular nonlocal sources

JOURNAL OF DIFFERENTIAL EQUATIONS, 409, 181–222.

A lower bound on the quantitative version of the transversality theorem

[Review of ]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 528(1).

A quantitative version of the transversality theorem

Communications in Mathematical Sciences.

Diffusion Approximations of Markovian Solutions to Discontinuous ODEs

Bressan, A., Mazzola, M., & Nguyen, K. T. (2023, March 5). JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS.

EXAMPLES AND CONJECTURES ON THE REGULARITY OF SOLUTIONS TO BALANCE LAWS

Ancona, F., Bianchini, S., Bressan, A., Colombo, R. M., & Nguyen, K. T. (2023, February 8). QUARTERLY OF APPLIED MATHEMATICS.

Generic Properties of First-Order Mean Field Games

Bressan, A., & Nguyen, K. T. T. (2023, January 2). DYNAMIC GAMES AND APPLICATIONS, Vol. 1.

STOCHASTIC EQUILIBRIUM SOLUTION FOR A DEBT MANAGEMENT PROBLEM WITH CURRENCY DEVALUATION

Marigonda, A., & Nguyen, K. T. (2023, May). MATHEMATICAL CONTROL AND RELATED FIELDS, Vol. 5.

A system of first order Hamilton-Jacobi equations related to an optimal debt management problem

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 29(4).

Generalized Differential Games

Barron, E. N., & Nguyen, K. T. (2022, May 21). DYNAMIC GAMES AND APPLICATIONS.

Metric Entropy for Hamilton--Jacobi Equations with Uniformly Directionally Convex Hamiltonian

SIAM Journal on Mathematical Analysis.

Shock interactions for the Burgers-Hilbert equation

Bressan, A., Galtung, S. T., Grunert, K., & Nguyen, K. T. (2022, June 24). COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, Vol. 6.

METRIC ENTROPY FOR FUNCTIONS OF BOUNDED TOTAL GENERALIZED VARIATION

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 53(1), 1168–1190.

Markovian Solutions to Discontinuous ODEs

Bressan, A., Mazzola, M., & Nguyen, K. T. (2021, March 12). JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS.

ON THE GLOBAL CONTROLLABILITY OF SCALAR CONSERVATION LAWS WITH BOUNDARY AND SOURCE CONTROLS

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 59(6), 4314–4338.

SBV regularity for Burgers-Poisson equation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 500(1).

A model of debt with bankruptcy risk and currency devaluation

Minimax Theory and Its Applications. https://www.heldermann.de/MTA/MTA05/MTA052/mta05014.htm

Quantitative compactness estimate for scalar conservation laws with nonconvex fluxes

Hyperbolic problems: theory, numerics, applications, 248–255. AIMS Ser. Appl. Math., 10.

APPROXIMATION OF SWEEPING PROCESSES AND CONTROLLABILITY FOR A SET-VALUED EVOLUTION

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 57(4), 2487–2514.

Lyapunov’s Theorem via Baire Category

In Springer INdAM Series (Vol. 32, pp. 181–194).

ON KOLMOGOROV ENTROPY COMPACTNESS ESTIMATES FOR SCALAR CONSERVATION LAWS WITHOUT UNIFORM CONVEXITY

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 51(4), 3020–3051.

Covering numbers for bounded variation functions

Journal of Mathematical Analysis and Applications, 468(2), 1131–1143.

Stability of Feedback Solutions for Infinite Horizon Noncooperative Differential Games

DYNAMIC GAMES AND APPLICATIONS, 8(1), 42–78.

A Stochastic Model of Optimal Debt Management and Bankruptcy

SIAM JOURNAL ON FINANCIAL MATHEMATICS, 8(1), 841–873.

Generalized Control Systems in the Space of Probability Measures

Set-Valued and Variational Analysis, 26(3), 663–691.

An equilibrium model of debt and bankruptcy

ESAIM: Control, Optimisation and Calculus of Variations, 22(4), 953–982.

COMPACTNESS ESTIMATES FOR HAMILTON-JACOBI EQUATIONS DEPENDING ON SPACE

Bulletin of the Institute of Mathematics Academia Sinica. https://www.math.sinica.edu.tw/bulletins/20161/2016104.pdf

Global existence of weak solutions for Burgers-Poisson equation

Journal of Differential Equations, 23(4), 23–46.

On the Burgers–Poisson equation

Journal of Differential Equations, 261(6), 3220–3246.

The bang–bang theorem via Baire category: a dual approach

Nonlinear Differential Equations and Applications NoDEA, 23(4).

The compactness estimates for Hamilton Jacobi Equations depending on space

Bulletin of the Institute of Mathematics, Academia Sinica, 11, 63–113.

Conservation law models for traffic flow on a network of roads

Networks and Heterogeneous Media, 10(2), 255–293.

On compactness estimates for general nonlinear system hyperbolic systems

Annales De l'Institut Henri Poincaré, Analyse Non Linéaire, 32(6), 1229–1257.

On compactness estimates for hyperbolic systems of conservation laws

Annales De l'Institut Henri Poincare (C) Non Linear Analysis, 32(6), 1229–1257.

Optima and equilibria for traffic flow on networks with backward propagating queues

Networks and Heterogeneous Media, 10(4), 717–748.

Optimality conditions and regularity results for time optimal control problems with differential inclusions

Journal of Mathematical Analysis and Applications, 427(1), 202–228.

Quantitative Compactness Estimates for Hamilton–Jacobi Equations

Archive for Rational Mechanics and Analysis, 219(2), 793–828.

BV Regularity and Differentiability Properties of a Class of Upper Semicontinuous Functions

In I. Lirkov, S. Margenov, & J. Waśniewski (Eds.), Large-Scale Scientific Computing: Vol. 8353 LNCS (pp. 116–124).

Global Existence of Weak Solutions for the Burgers--Hilbert Equation

SIAM Journal on Mathematical Analysis, 46(4), 2884–2904.

On quantitative compactness estimates for hyperbolic conservation laws

Hyperbolic problems: theory, numerics, applications, 249–257, AIMS Ser. Appl. Math., 8, Am. Inst. Math. Sci. (AIMS), Springfield, MO,

Non-Lipschitz points and the SBV regularity of the minimum time function

Calculus of Variations and Partial Differential Equations, 51(1-2), 439–463.

On the minimum time function around the origin

Mathematical Control and Related Fields, 3(1), 51–82.

Some regularity results for a class of upper semicontinuous functions

Indiana University Mathematics Journal, 62(1), 45–89.

Lower compactness estimates for scalar balance laws

Communications on Pure and Applied Mathematics, 65(9), 1303–1329.

Rectifiability of special singularities of non-lipschitz functions

Journal of Convex Analysis, 19(1), 159–170. http://www.scopus.com/inward/record.url?eid=2-s2.0-84856829336&partnerID=MN8TOARS

Singular gradient flow of the distance function and homotopy equivalence

Mathematische Annalen, 356(1), 23–43.

Exterior Sphere Condition and Time Optimal Control for Differential Inclusions

SIAM Journal on Control and Optimization, 49(6), 2558–2576.

Hypographs satisfying an external sphere condition and the regularity of the minimum time function

Journal of Mathematical Analysis and Applications, 372(2), 611–628.

On the Structure of the Minimum Time Function

SIAM Journal on Control and Optimization, 48(7), 4776–4814.

Quantitative isoperimetric inequalities for a class of nonconvex sets

Calculus of Variations and Partial Differential Equations, 37(1-2), 141–166.

CRITICAL POINTS OF NON-C2 FUNCTIONALS

Topological Methods in Nonlinear Analysis.

Critical points of non-C2 functional

Topological Methods of Nonlinear Analysis, 29(1), 35–68.

Morse-Palais Lemma for nonsmooth functionals on normed spaces

Proceedings of the American Mathematical Society, 135(3), 921–927.

Morse-palais lemma for nonsmooth functionals on normed spaces

Proceedings of the American Mathematical Society, 135(3), 921–927.