Zobrazeno 1 - 10
of 146
pro vyhledávání: '"Nguyen, Khai T"'
Autor:
Bressan, Alberto, Nguyen, Khai T.
The paper is concerned with a scalar balance law, where the source term depends on a control function $\alpha(t)$. Given a control $\alpha\in \mathbf{L}^\infty\bigl([0,T]\bigr)$, it is proved that, for generic initial data $\bar u \in \mathcal{C}^3(\
Externí odkaz:
http://arxiv.org/abs/2410.20032
Publikováno v:
J. Differential Equations 409 (2024), 181--222
The present paper establishes a local well-posed result for piecewise regular solutions with single shock of scalar balance laws with singular integral of convolution type kernels. In a neighborhood of the shock curve, a detailed description of the s
Externí odkaz:
http://arxiv.org/abs/2409.01703
In this paper, we study an optimal exit time problem with general running and terminal costs and a target $\mathcal{S}\subset\mathbb{R}^d$ having an inner ball property for a nonlinear control system that satisfies mild controllability assumptions. I
Externí odkaz:
http://arxiv.org/abs/2406.06409
Autor:
Murdza, Andrew, Nguyen, Khai T.
The paper establishes a sharp quantitative estimate for the $(d-1)$-Hausdorff measure of the critical set of $\mathcal{C}^1$ vector-valued functions on $\mathbb{R}^d$. Additionally, we prove that for a generic $\mathcal{C}^2$ function where ``generic
Externí odkaz:
http://arxiv.org/abs/2405.17107
The first part of the paper studies a class of optimal control problems in Bolza form, where the dynamics is linear w.r.t.~the control function. A necessary condition is derived, for the optimality of a trajectory which starts at a conjugate point. T
Externí odkaz:
http://arxiv.org/abs/2404.02080
The paper provides an elementary proof establishing a sharp universal bound on the $(d-1)$-Hausdorff measure of the zeros of any nontrivial multivariable polynomial $p:\mathbb{R}^d\to\mathbb{R}$ within a $d$-dimensional cube of size $r$. This bound d
Externí odkaz:
http://arxiv.org/abs/2312.17462
Autor:
Murdza, Andrew, Nguyen, Khai T.
The present paper studies a quantitative version of the transversality theorem. More precisely, given a continuous function $f\in \mathcal{C}([0,1]^d,\mathbb{R}^m)$ and a manifold $W\subset \mathbb{R}^m$ of dimension $p$, a sharpness result on the up
Externí odkaz:
http://arxiv.org/abs/2301.00432
Autor:
Bressan, Alberto, Nguyen, Khai T.
We consider a class of deterministic mean field games, where the state associated with each player evolves according to an ODE which is linear w.r.t. the control. Existence, uniqueness, and stability of solutions are studied from the point of view of
Externí odkaz:
http://arxiv.org/abs/2210.14643
Publikováno v:
Comm. Partial Differential Equations 47, 1795-1844 (2022)
This paper provides an asymptotic description of a solution to the Burgers-Hilbert equation in a neighborhood of a point where two shocks interact. The solution is obtained as the sum of a function with $H^2$ regularity away from the shocks plus a co
Externí odkaz:
http://arxiv.org/abs/2204.02421
Autor:
Murdza, Andrew, Nguyen, Khai T.
The present paper studies a quantitative version of the transversality theorem. More precisely, given a continuous function $g\in \mathcal{C}([0,1]^d,\mathbb{R}^m)$ and a global smooth manifold $W\subset \mathbb{R}^m$ of dimension $p$, we establish a
Externí odkaz:
http://arxiv.org/abs/2112.07107