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*.

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.

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).

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*.

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.

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.

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^{*}

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 ^{*}

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

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 ^{*}

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 ^{*}

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 ^{*}

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

Updated: September 8th, 2019 18:32

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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