Works (54)
Updated: November 2nd, 2024 05:03
2024 article
GENERIC PROPERTIES OF CONJUGATE POINTS IN OPTIMAL CONTROL PROBLEMS
Bressan, A., Mazzola, M., & Nguyen, K. t. (2024, September). MATHEMATICAL CONTROL AND RELATED FIELDS.
author keywords: Optimal control problem; necessary optimality condition; conjugate point; generic property; Baire category
open access via doi.org (publisher)
Sources: ORCID, Web Of Science
Added: September 23, 2024
2024 journal article
Piecewise regular solutions to scalar balance laws with singular nonlocal sources
JOURNAL OF DIFFERENTIAL EQUATIONS, 409, 181–222.
author keywords: Piecewise smooth solutions; Scalar balance law; Singular kernels; Shock
Sources: ORCID, Web Of Science, NC State University Libraries
Added: July 22, 2024
2024 article
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.
author keywords: Stochastic model; infinite time horizon; optimal feedback solution; debt management; currency devaluation
Sources: Web Of Science, NC State University Libraries
Added: June 19, 2023
2023 review
A lower bound on the quantitative version of the transversality theorem
[Review of ]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 528(1).
author keywords: Transversality lemma; Quantitative estimates
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: ORCID, Web Of Science
Added: August 14, 2023
2023 journal article
A quantitative version of the transversality theorem
Communications in Mathematical Sciences.
Source: ORCID
Added: October 31, 2024
2023 article
Diffusion Approximations of Markovian Solutions to Discontinuous ODEs
Bressan, A., Mazzola, M., & Nguyen, K. T. (2023, March 5). JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS.
UN Sustainable Development Goal Categories
13. Climate Action
(Web of Science)
Sources: ORCID, Web Of Science
Added: March 27, 2023
2023 article
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.
UN Sustainable Development Goal Categories
15. Life on Land
(OpenAlex)
Sources: ORCID, Web Of Science
Added: March 13, 2023
2023 article
Generic Properties of First-Order Mean Field Games
Bressan, A., & Nguyen, K. T. T. (2023, January 2). DYNAMIC GAMES AND APPLICATIONS, Vol. 1.
Sources: Web Of Science, NC State University Libraries
Added: January 17, 2023
2022 journal article
A system of first order Hamilton-Jacobi equations related to an optimal debt management problem
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 29(4).
author keywords: Hamilton-Jacobi equations; Viscosity solutions; Deterministic optimal debt management; Equilibrium solutions
Sources: ORCID, Web Of Science
Added: June 27, 2022
2022 article
Generalized Differential Games
Barron, E. N., & Nguyen, K. T. (2022, May 21). DYNAMIC GAMES AND APPLICATIONS.
author keywords: Differential games; Isaacs' equation; Generalized game; Hamilton-Jacobi; Viscosity solution; Control constraints
Sources: ORCID, Web Of Science
Added: May 31, 2022
2022 journal article
Metric Entropy for Hamilton--Jacobi Equations with Uniformly Directionally Convex Hamiltonian
SIAM Journal on Mathematical Analysis.
Source: ORCID
Added: August 15, 2024
2022 article
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.
author keywords: Burgers-Hilbert equation; weak solution; piecewise regular solution; shock interaction
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(OpenAlex)
13. Climate Action
(Web of Science)
Sources: Web Of Science, NC State University Libraries, ORCID
Added: July 5, 2022
2021 journal article
METRIC ENTROPY FOR FUNCTIONS OF BOUNDED TOTAL GENERALIZED VARIATION
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 53(1), 1168–1190.
author keywords: metric entropy; doubling dimension; total generalized variation
TL;DR:
A sharp estimate is established for a minimal number of binary digits needed to represent all bounded total generalized variation functions taking values in a general totally bounded metric space up to an accuracy of $\varepsilon>0$ with respect to the ${\bf L}^1$-distance.
(via Semantic Scholar)
Sources: ORCID, Web Of Science
Added: March 29, 2021
2021 article
Markovian Solutions to Discontinuous ODEs
Bressan, A., Mazzola, M., & Nguyen, K. T. (2021, March 12). JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS.
UN Sustainable Development Goal Categories
13. Climate Action
(Web of Science)
Sources: ORCID, Web Of Science
Added: April 5, 2021
2021 journal article
ON THE GLOBAL CONTROLLABILITY OF SCALAR CONSERVATION LAWS WITH BOUNDARY AND SOURCE CONTROLS
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 59(6), 4314–4338.
author keywords: conservation laws; source control; global exact controllability; return method
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(Web of Science)
15. Life on Land
(OpenAlex)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: January 10, 2022
2021 journal article
SBV regularity for Burgers-Poisson equation
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 500(1).
author keywords: Burgers-Poisson equation; Entropy weak solution; SBV regularity
Sources: Web Of Science, ORCID, NC State University Libraries
Added: April 19, 2021
2020 journal article
A model of debt with bankruptcy risk and currency devaluation
Minimax Theory and Its Applications. https://www.heldermann.de/MTA/MTA05/MTA052/mta05014.htm
Source: ORCID
Added: October 31, 2024
2019 journal article
APPROXIMATION OF SWEEPING PROCESSES AND CONTROLLABILITY FOR A SET-VALUED EVOLUTION
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 57(4), 2487–2514.
Contributors: A. Bressan *, M. Mazzola * & K. Nguyen *
author keywords: sweeping processes; set-valued evolution; controllability
TL;DR:
Under suitable assumptions, it is proved that there exists a control function such that the corresponding evolution of the set $\Omega(t)$ is arbitrarily close to the one determined by the sweeping process.
(via Semantic Scholar)
Sources: ORCID, Web Of Science
Added: April 20, 2020
2019 book
Lyapunov’s Theorem via Baire Category
In Springer INdAM Series (Vol. 32, pp. 181–194).
Contributors: M. Mazzola * & K. Nguyen n
Source: ORCID
Added: April 22, 2020
2019 journal article
ON KOLMOGOROV ENTROPY COMPACTNESS ESTIMATES FOR SCALAR CONSERVATION LAWS WITHOUT UNIFORM CONVEXITY
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 51(4), 3020–3051.
Contributors: F. Ancona *, O. Glass* & K. Nguyen n
author keywords: Kolmogorov entropy; scalar conservation laws; compactness estimates
TL;DR:
This paper provides an extension of quantitative compactness estimates to the case of scalar conservation laws with a smooth flux function that either is strictly (but not necessarily uniformly) convex or has a single inflection point with a polynomial degeneracy.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
15. Life on Land
(OpenAlex)
Sources: ORCID, Web Of Science
Added: April 20, 2020
2018 journal article
Covering numbers for bounded variation functions
Journal of Mathematical Analysis and Applications, 468(2), 1131–1143.
Contributors: P. Dutta n & K. Nguyen n
author keywords: The epsilon-entropy; Bounded variation functions
TL;DR:
Upper and lower estimates for the minimal number of functions needed to represent a bounded variation function with an accuracy of epsilon with respect to ${\bf L}^1$-distance are provided.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
Sources: Crossref, ORCID, NC State University Libraries, Web Of Science
Added: October 16, 2018
2017 journal article
A Stochastic Model of Optimal Debt Management and Bankruptcy
SIAM JOURNAL ON FINANCIAL MATHEMATICS, 8(1), 841–873.
Contributors: A. Bressan, A. Marigonda *, K. Nguyen n & M. Palladino *
author keywords: debt management and bankruptcy; infinite time horizon; optimal feedback solution
TL;DR:
For a given bankruptcy threshold, existence and properties of optimal feedback strategies for the borrower are studied, in a stochastic framework as well as in a limit deterministic setting.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
8. Decent Work and Economic Growth
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2017 journal article
Generalized Control Systems in the Space of Probability Measures
Set-Valued and Variational Analysis, 26(3), 663–691.
Contributors: G. Cavagnari *, A. Marigonda *, K. Nguyen n & F. Priuli*
author keywords: Optimal transport; Differential inclusions; Time-optimal control; Set-valued analysis
Sources: ORCID, Crossref, NC State University Libraries
Added: June 30, 2019
2016 journal article
An equilibrium model of debt and bankruptcy
ESAIM: Control, Optimisation and Calculus of Variations, 22(4), 953–982.
Contributors: A. Bressan * & K. Nguyen *
author keywords: Optimal control; differential game; optimal debt management; bankruptcy risk
Sources: Crossref, ORCID, NC State University Libraries
Added: June 30, 2019
2016 journal article
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
Source: ORCID
Added: October 31, 2024
2016 journal article
Global existence of weak solutions for Burgers-Poisson equation
Journal of Differential Equations, 23(4), 23–46.
Source: NC State University Libraries
Added: June 30, 2019
2016 journal article
On the Burgers–Poisson equation
Journal of Differential Equations, 261(6), 3220–3246.
Contributors: K. Grunert * & K. Nguyen *
author keywords: Burgers-Poisson equation; Existence; Uniqueness; Blow-up
Sources: ORCID, Crossref, NC State University Libraries
Added: April 22, 2020
2016 journal article
Stability of Feedback Solutions for Infinite Horizon Noncooperative Differential Games
DYNAMIC GAMES AND APPLICATIONS, 8(1), 42–78.
Contributors: A. Bressan * & K. Nguyen n
author keywords: Noncooperative differential games; Nash equilibrium; Infinite horizon
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2016 journal article
The bang–bang theorem via Baire category: a dual approach
Nonlinear Differential Equations and Applications NoDEA, 23(4).
Contributors: A. Bressan *, M. Mazzola * & K. Nguyen *
Sources: Crossref, ORCID, NC State University Libraries
Added: June 30, 2019
2016 journal article
The compactness estimates for Hamilton Jacobi Equations depending on space
Bulletin of the Institute of Mathematics, Academia Sinica, 11, 63–113.
Source: NC State University Libraries
Added: June 30, 2019
2015 journal article
Conservation law models for traffic flow on a network of roads
Networks and Heterogeneous Media, 10(2), 255–293.
Contributors: A. Bressan & K. Nguyen *
author keywords: Traffic flows; network of roads; scalar conservation laws; Hamilton Jacobi equations; Lax type formula
TL;DR:
A model of traffic flow near an intersection, where drivers seeking to enter a congested road wait in a buffer of limited capacity, achieves well-posedness for general $L^\infty $ data, and continuity w.r.t. weak convergence of the initial densities.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(OpenAlex)
Sources: Crossref, ORCID, NC State University Libraries
Added: June 30, 2019
2015 journal article
On compactness estimates for general nonlinear system hyperbolic systems
Annales De l'Institut Henri Poincaré, Analyse Non Linéaire, 32(6), 1229–1257.
Source: NC State University Libraries
Added: July 28, 2019
2015 journal article
Optima and equilibria for traffic flow on networks with backward propagating queues
Networks and Heterogeneous Media, 10(4), 717–748.
Contributors: A. Bressan * & K. Nguyen *
author keywords: Traffic flows; network of roads; scalar conservation laws; global optima; Nash equilibria
TL;DR:
Two main results are proved: the existence of a globally optimal solution, minimizing the sum of the costs to all drivers, and the existenceof a Nash equilibrium solution, where no driver can lower his own cost by changing his departure time or the route taken to reach destination.
(via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: June 30, 2019
2015 journal article
Optimality conditions and regularity results for time optimal control problems with differential inclusions
Journal of Mathematical Analysis and Applications, 427(1), 202–228.
Contributors: P. Cannarsa *, A. Marigonda * & K. Nguyen *
author keywords: Proximal normal vectors; Differential inclusions; Time optimal control; Semiconcave functions
Sources: Crossref, ORCID, NC State University Libraries
Added: June 30, 2019
2015 journal article
Quantitative Compactness Estimates for Hamilton–Jacobi Equations
Archive for Rational Mechanics and Analysis, 219(2), 793–828.
Contributors: F. Ancona *, P. Cannarsa * & K. Nguyen *
UN Sustainable Development Goal Categories
15. Life on Land
(OpenAlex)
Sources: ORCID, Crossref, NC State University Libraries
Added: June 30, 2019
2014 chapter
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).
Contributors: A. Marigonda *, K. Nguyen * & D. Vittone *
Ed(s): I. Lirkov, S. Margenov & J. Waśniewski
Event: 9th International Conference, LSSC 2013 at Sozopol, Bulgaria on June 3-7, 2013
TL;DR:
A class of upper semicontinuous functions whose hypograph satisfies a geometric regularity property, namely: there exist \(\theta \in ]0,1] such that for each \(P\) on the boundary of \(\mathrm {hypo}\,f\) there exists a unitary Frechet (outer) normal.
(via Semantic Scholar)
Sources: ORCID, Crossref, NC State University Libraries
Added: April 22, 2020
2014 journal article
Global Existence of Weak Solutions for the Burgers--Hilbert Equation
SIAM Journal on Mathematical Analysis, 46(4), 2884–2904.
Contributors: A. Bressan & K. Nguyen *
author keywords: Burgers-Hilbert equations; weak entropy solutions; global existence
TL;DR:
This paper establishes the global existence of weak solutions to the Burgers--Hilbert equation, for general initial data in L for positive times, and a partial uniqueness result is proved for spatially periodic solutions.
(via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: June 30, 2019
2014 journal article
On compactness estimates for hyperbolic systems of conservation laws
Annales De l'Institut Henri Poincare (C) Non Linear Analysis, 32(6), 1229–1257.
Contributors: F. Ancona *, O. Glass* & K. Nguyen *
author keywords: Hyperbolic systems of conservation laws; Temple systems; Compactness estimates; Kolmogorov entropy
UN Sustainable Development Goal Categories
15. Life on Land
(OpenAlex)
Sources: ORCID, Crossref, NC State University Libraries
Added: April 22, 2020
2014 conference paper
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,
Source: ORCID
Added: April 22, 2020
2013 journal article
Non-Lipschitz points and the SBV regularity of the minimum time function
Calculus of Variations and Partial Differential Equations, 51(1-2), 439–463.
Contributors: G. Colombo *, K. Nguyen * & L. Nguyen *
Sources: ORCID, Crossref, NC State University Libraries
Added: July 9, 2019
2013 journal article
On the minimum time function around the origin
Mathematical Control and Related Fields, 3(1), 51–82.
Contributors: G. Colombo * & K. Nguyen *
author keywords: Reachable sets; exterior sphere condition; maximum principle
Sources: Crossref, ORCID, NC State University Libraries
Added: June 30, 2019
2013 journal article
Some regularity results for a class of upper semicontinuous functions
Indiana University Mathematics Journal, 62(1), 45–89.
Contributors: A. Marigonda *, K. Nguyen * & D. Vittone *
author keywords: exterior sphere condition; sets with positive reach; reduced boundary
Sources: Crossref, ORCID, NC State University Libraries
Added: June 30, 2019
2012 journal article
Lower compactness estimates for scalar balance laws
Communications on Pure and Applied Mathematics, 65(9), 1303–1329.
Contributors: F. Ancona *, O. Glass* & K. Nguyen *
UN Sustainable Development Goal Categories
15. Life on Land
(OpenAlex)
Sources: Crossref, ORCID, NC State University Libraries
Added: June 30, 2019
2012 journal article
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
Contributors: K. Nguyen & D. Vittone
Sources: NC State University Libraries, ORCID
Added: July 28, 2019
2012 journal article
Singular gradient flow of the distance function and homotopy equivalence
Mathematische Annalen, 356(1), 23–43.
Contributors: P. Albano *, P. Cannarsa *, K. Nguyen * & C. Sinestrari *
Sources: ORCID, Crossref, NC State University Libraries
Added: June 30, 2019
2011 journal article
Exterior Sphere Condition and Time Optimal Control for Differential Inclusions
SIAM Journal on Control and Optimization, 49(6), 2558–2576.
Contributors: P. Cannarsa * & K. Nguyen
author keywords: proximal normal vectors; exterior sphere condition; differential inclusions; time optimal control; semiconcave functions
TL;DR:
It is proved that the hypograph of $T(\cdot)$ satisfies, locally, an exterior sphere condition, which ensures most of the regularity results that hold for semiconcave functions, without assuming $T \cdot$ to be Lipschitz.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
10. Reduced Inequalities
(OpenAlex)
Sources: Crossref, ORCID, NC State University Libraries
Added: June 30, 2019
2010 journal article
Hypographs satisfying an external sphere condition and the regularity of the minimum time function
Journal of Mathematical Analysis and Applications, 372(2), 611–628.
Contributors: K. Nguyen *
author keywords: Normal vectors; phi-convex (prox-regular, positive reach) sets; Internal/external sphere condition
Sources: Crossref, ORCID, NC State University Libraries
Added: June 30, 2019
2010 journal article
On the Structure of the Minimum Time Function
SIAM Journal on Control and Optimization, 48(7), 4776–4814.
Contributors: G. Colombo * & K. Nguyen *
author keywords: normal vectors; phi-convex (prox-regular, positive reach) sets; internal sphere condition; small time controllability; adjoint flow
TL;DR:
It is shown thathypo(T) is $\varphi-convex$- Convex, i.e., satisfies a strong external sphere condition, and is a.e. twice differentiable and satisfies some further regularity properties.
(via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: June 30, 2019
2009 journal article
Quantitative isoperimetric inequalities for a class of nonconvex sets
Calculus of Variations and Partial Differential Equations, 37(1-2), 141–166.
Contributors: G. Colombo * & K. Nguyen *
author keywords: Sets with positive reach; External sphere condition; Internal cone condition; Isoperimetric deficiency; Spherical deviation; Fraenkel asymmetry
Sources: Crossref, ORCID, NC State University Libraries
Added: June 30, 2019
2007 journal article
CRITICAL POINTS OF NON-C2 FUNCTIONALS
Topological Methods in Nonlinear Analysis.
Source: ORCID
Added: April 22, 2020
2007 journal article
Critical points of non-C2 functional
Topological Methods of Nonlinear Analysis, 29(1), 35–68.
Source: NC State University Libraries
Added: July 9, 2019
2007 journal article
Morse-Palais Lemma for nonsmooth functionals on normed spaces
Proceedings of the American Mathematical Society, 135(3), 921–927.
Source: NC State University Libraries
Added: July 28, 2019
2006 journal article
Morse-palais lemma for nonsmooth functionals on normed spaces
Proceedings of the American Mathematical Society, 135(3), 921–927.
Contributors: D. Duc*, T. Hung* & N. Khai *
author keywords: Morse-Palais lemma; normed spaces; directional differentiability
Source: ORCID
Added: April 22, 2020
Employment
Updated: September 8th, 2019 18:32
North Carolina State Univeristy Raleigh, US
Department of Mathematics
Funding History
Funding history based on the linked ORCID record. Updated: October 31st, 2024 11:05
grant
September 1, 2022 - August 1, 2025
Generic Singularities and Fine Regularity Structure for Nonlinear Partial Differential Equations
NSF
grant
August 1, 2022 - July 1, 2023
40th Southeastern-Atlantic Regional Conference on Differential Equations
NSF
grant
September 1, 2017 - August 1, 2022
Nonlinear PDEs, Differential Games and Applications
Simons Foundation
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