The Experts below are selected from a list of 66312 Experts worldwide ranked by ideXlab platform
Yongqian Zhang - One of the best experts on this subject based on the ideXlab platform.
-
Two-Dimensional Steady Supersonic Exothermically Reacting Euler Flow past Lipschitz Bending Walls
SIAM Journal on Mathematical Analysis, 2017Co-Authors: Gui-qiang G. Chen, Jie Kuang, Yongqian ZhangAbstract:We are concerned with the two-dimensional steady supersonic reacting Euler flow past Lipschitz bending walls that are small perturbations of a convex one, and establish the existence of global entropy solutions when the total variation of both the initial data and the slope of the boundary is sufficiently small. The flow is governed by an ideal polytropic gas and undergoes a one-step exothermic chemical reaction under the reaction rate function that is Lipschtiz and has a positive lower bound. The heat released by the reaction may cause the total variation of the solution to increase along the flow direction. We employ the modified wavefront tracking scheme to construct approximate solutions and develop a Glimm-type functional by incorporating the approximate strong rarefaction waves and Lipschitz bending walls to obtain the uniform bound on the total variation of the approximate solutions. Then we employ this bound to prove the convergence of the approximate solutions to a global entropy solution that co...
-
Two-Dimensional Steady Supersonic Exothermically Reacting Euler Flow past Lipschitz Bending Walls
arXiv: Analysis of PDEs, 2015Co-Authors: Gui-qiang G. Chen, Jie Kuang, Yongqian ZhangAbstract:We are concerned with the two-dimensional steady supersonic reacting Euler flow past Lipschitz bending walls that are small perturbations of a convex one, and establish the existence of global entropy solutions when the total variation of both the initial data and the slope of the boundary is sufficiently small. The flow is governed by an ideal polytropic gas and undergoes a one-step exothermic chemical reaction under the reaction rate function that is Lipschtiz and has a positive lower bound. The heat released by the reaction may cause the total variation of the solution to increase along the flow direction. We employ the modified wave-front tracking scheme to construct approximate solutions and develop a Glimm-type functional by incorporating the approximate strong rarefaction waves and Lipschitz bending walls to obtain the uniform bound on the total variation of the approximate solutions. Then we employ this bound to prove the convergence of the approximate solutions to a global entropy solution that contains a strong rarefaction wave generated by the Lipschitz bending wall. In addition, the asymptotic behavior of the entropy solution in the flow direction is also analyzed.
Gui-qiang G. Chen - One of the best experts on this subject based on the ideXlab platform.
-
Two-Dimensional Steady Supersonic Exothermically Reacting Euler Flow past Lipschitz Bending Walls
SIAM Journal on Mathematical Analysis, 2017Co-Authors: Gui-qiang G. Chen, Jie Kuang, Yongqian ZhangAbstract:We are concerned with the two-dimensional steady supersonic reacting Euler flow past Lipschitz bending walls that are small perturbations of a convex one, and establish the existence of global entropy solutions when the total variation of both the initial data and the slope of the boundary is sufficiently small. The flow is governed by an ideal polytropic gas and undergoes a one-step exothermic chemical reaction under the reaction rate function that is Lipschtiz and has a positive lower bound. The heat released by the reaction may cause the total variation of the solution to increase along the flow direction. We employ the modified wavefront tracking scheme to construct approximate solutions and develop a Glimm-type functional by incorporating the approximate strong rarefaction waves and Lipschitz bending walls to obtain the uniform bound on the total variation of the approximate solutions. Then we employ this bound to prove the convergence of the approximate solutions to a global entropy solution that co...
-
Two-Dimensional Steady Supersonic Exothermically Reacting Euler Flow past Lipschitz Bending Walls
arXiv: Analysis of PDEs, 2015Co-Authors: Gui-qiang G. Chen, Jie Kuang, Yongqian ZhangAbstract:We are concerned with the two-dimensional steady supersonic reacting Euler flow past Lipschitz bending walls that are small perturbations of a convex one, and establish the existence of global entropy solutions when the total variation of both the initial data and the slope of the boundary is sufficiently small. The flow is governed by an ideal polytropic gas and undergoes a one-step exothermic chemical reaction under the reaction rate function that is Lipschtiz and has a positive lower bound. The heat released by the reaction may cause the total variation of the solution to increase along the flow direction. We employ the modified wave-front tracking scheme to construct approximate solutions and develop a Glimm-type functional by incorporating the approximate strong rarefaction waves and Lipschitz bending walls to obtain the uniform bound on the total variation of the approximate solutions. Then we employ this bound to prove the convergence of the approximate solutions to a global entropy solution that contains a strong rarefaction wave generated by the Lipschitz bending wall. In addition, the asymptotic behavior of the entropy solution in the flow direction is also analyzed.
Prats Martí - One of the best experts on this subject based on the ideXlab platform.
-
Triebel-Lizorkin regularity and bi-Lipschitz maps: composition operator and inverse function regularity
2021Co-Authors: Prats MartíAbstract:We study the stability of Triebel-Lizorkin regularity of bounded functions and Lipschitz functions under bi-Lipschitz changes of variables and the regularity of the inverse function of a Triebel-Lizorkin bi-Lipschitz map in Lipschitz domains. To obtain the results we provide an equivalent norm for the Triebel-Lizorkin spaces with fractional smoothness in uniform domains in terms of the first-order difference of the last weak derivative available averaged on balls.Comment: 34 pages, 1 figur
-
Triebel-Lizorkin regularity and bi-Lipschitz maps: composition operator and inverse function regularity
2020Co-Authors: Prats MartíAbstract:We study the stability of Triebel-Lizorkin regularity of bounded functions and Lipschitz functions under bi-Lipschitz changes of variables and the regularity of the inverse function of a Triebel-Lizorkin bi-Lipschitz map in Lipschitz domains. To obtain our results we provide an equivalent norm for the Triebel-Lizorkin spaces with fractional smoothness in uniform domains in terms of the first-order difference of the last weak derivative available averaged on balls.Comment: 34 pages, 1 figur
Alexandros G Dimakis - One of the best experts on this subject based on the ideXlab platform.
-
exactly computing the local Lipschitz constant of relu networks
Neural Information Processing Systems, 2020Co-Authors: Matt Jordan, Alexandros G DimakisAbstract:The local Lipschitz constant of a neural network is a useful metric with applications in robustness, generalization, and fairness evaluation. We provide novel analytic results relating the local Lipschitz constant of nonsmooth vector-valued functions to a maximization over the norm of the generalized Jacobian. We present a sufficient condition for which backpropagation always returns an element of the generalized Jacobian, and reframe the problem over this broad class of functions. We show strong inapproximability results for estimating Lipschitz constants of ReLU networks, and then formulate an algorithm to compute these quantities exactly. We leverage this algorithm to evaluate the tightness of competing Lipschitz estimators and the effects of regularized training on the Lipschitz constant.
Jie Kuang - One of the best experts on this subject based on the ideXlab platform.
-
Two-Dimensional Steady Supersonic Exothermically Reacting Euler Flow past Lipschitz Bending Walls
SIAM Journal on Mathematical Analysis, 2017Co-Authors: Gui-qiang G. Chen, Jie Kuang, Yongqian ZhangAbstract:We are concerned with the two-dimensional steady supersonic reacting Euler flow past Lipschitz bending walls that are small perturbations of a convex one, and establish the existence of global entropy solutions when the total variation of both the initial data and the slope of the boundary is sufficiently small. The flow is governed by an ideal polytropic gas and undergoes a one-step exothermic chemical reaction under the reaction rate function that is Lipschtiz and has a positive lower bound. The heat released by the reaction may cause the total variation of the solution to increase along the flow direction. We employ the modified wavefront tracking scheme to construct approximate solutions and develop a Glimm-type functional by incorporating the approximate strong rarefaction waves and Lipschitz bending walls to obtain the uniform bound on the total variation of the approximate solutions. Then we employ this bound to prove the convergence of the approximate solutions to a global entropy solution that co...
-
Two-Dimensional Steady Supersonic Exothermically Reacting Euler Flow past Lipschitz Bending Walls
arXiv: Analysis of PDEs, 2015Co-Authors: Gui-qiang G. Chen, Jie Kuang, Yongqian ZhangAbstract:We are concerned with the two-dimensional steady supersonic reacting Euler flow past Lipschitz bending walls that are small perturbations of a convex one, and establish the existence of global entropy solutions when the total variation of both the initial data and the slope of the boundary is sufficiently small. The flow is governed by an ideal polytropic gas and undergoes a one-step exothermic chemical reaction under the reaction rate function that is Lipschtiz and has a positive lower bound. The heat released by the reaction may cause the total variation of the solution to increase along the flow direction. We employ the modified wave-front tracking scheme to construct approximate solutions and develop a Glimm-type functional by incorporating the approximate strong rarefaction waves and Lipschitz bending walls to obtain the uniform bound on the total variation of the approximate solutions. Then we employ this bound to prove the convergence of the approximate solutions to a global entropy solution that contains a strong rarefaction wave generated by the Lipschitz bending wall. In addition, the asymptotic behavior of the entropy solution in the flow direction is also analyzed.