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Weak Continuity and Compactness for Nonlinear Partial Differential Equations

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Chinese Annals of Mathematics,Series B 2015年第5期36卷 715-736页

作者： gui-Qiang g.chen School of Mathematical Sciences Fudan University Academy of Mathematics and Systems Science Chinese Academy of Sciences Mathematical Institute University of Oxford

This paper presents several examples of fundamental problems involving weak continuity and compactness for nonlinear partial differential equations, in which compensated compactness and related ideas have played a significant role. The compactness and convergence of vanishing viscosity solutions for nonlinear hyperbolic conservation laws are first analyzed, including the inviscid limit from the Navier-Stokes equations to the Euler equations for homentropic flow, the vanishing viscosity method to construct the global spherically symmetric solutions to the multidimensional compressible Euler equations, and the sonic-subsonic limit of solutions of the full Euler equations for multi-dimensional steady compressible fluids. Then the weak continuity and rigidity of the gauss-Codazzi-Ricci system and corresponding isometric embeddings in differential geometry are revealed. Further references are also provided for some recent developments on the weak continuity and compactness for nonlinear partial differential equations.

关键词： Weak continuity Compensated compactness Nonlinear partial differential equations Euler equations gauss-Codazzi-Ricci system

Two-Dimensional Riemann Problems:Transonic Shock Waves and Free Boundary Problems

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Communications on Applied Mathematics and Computation 2023年第3期5卷 1015-1052页

作者： gui-Qiang g.chen Oxford Centre for Nonlinear PDE Mathematical InstituteUniversity of OxfordOxford OX26GGUK

We are concerned with global solutions of multidimensional(M-D)Riemann problems for nonlinear hyperbolic systems of conservation laws,focusing on their global configurations and *** present some recent developments in the rigorous analysis of two-dimensional(2-D)Riemann problems involving transonic shock waves through several prototypes of hyperbolic systems of conservation laws and discuss some further M-D Riemann problems and related problems for nonlinear partial differential *** particular,we present four different 2-D Riemann problems through these prototypes of hyperbolic systems and show how these Riemann problems can be reformulated/solved as free boundary problems with transonic shock waves as free boundaries for the corresponding nonlinear conservation laws of mixed elliptic-hyperbolic type and related nonlinear partial differential equations.

关键词： Riemann problems Two-dimensional(2-D) Transonic shocks Solution structure Free boundary problems Mixed elliptic-hyperbolic type global configurations Large-time asymptotics global attractors Multidimensional(M-D) Shock capturing methods

Tuning catalytic properties using an atomically dispersed metal overlayer on transition metal carbide substrates

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National Science Review 2017年第6期4卷 788-789页

作者： Jingguang g.chen Chemistry Department Brookhaven National Laboratory Department of Chemical Engineering Columbia University

Aqueous-phase reforming of methanol(APRM)represents an important reaction to produce hydrogen for lowtemperature polymer electrode membrane(PEM)hydrogen fuel *** ideal catalyst for APRM should show high activity towar... 详细信息

关键词： PgM TMC Tuning catalytic properties using an atomically dispersed metal overlayer on transition metal carbide substrates Pt

Challenges and opportunities in plasma-activated reactions of CO_(2) with light alkanes

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Journal of Energy Chemistry 2023年第9期84卷 424-427页

作者： Lea R.Winter Jingguang g.chen Department of Chemical and Environmental Engineering Yale UniversityNew HavenCT 06520United States Department of Chemical Engineering Columbia UniversityNew YorkNY 10027United States Chemistry Division Brookhaven National LaboratoryUptonNY 11973United States

Mitigation of the deleterious environmental impacts associated with CO_(2) emissions requires the development of more sustainable processes for synthesizing fuels and *** conversion of abundant yet difficult to activate molecules such as CO_(2) and surplus light alkanes from shale gas to desirable products can potentially reduce reliance upon conventional fossil-based ***,co-conversion of CO_(2) with abundant light alkanes such as methane and ethane using atmospheric-pressure.

关键词： alkanes methane synthesizing

Further numerical investigation on concrete dynamic behaviors with considering stress non-equilibrium in SHPB test based on the waveform features

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Acta Mechanica Sinica 2020年第4期36卷 873-886页

作者： T.H.Lv X.W.chen Y.J.Deng g.chen State Key Laboratory of Explosion Science and Technology Beijing Institute of TechnologyBeijing 100081China Advanced Research Institute of Multidisciplinary Science Beijing Institute of TechnologyBeijing 100081China Shock and Vibration of Engineering Materials and Structures Key Laboratory of Sichuan Province Southwest University of Science and TechnologyMianyang 621000China Institute of Systems Engineering China Academy of Engineering PhysicsMianyang 621999China

In this study,with the meso-scale model reliably validated in our previous work(Construction and Building Materials,2018),the waveform features of plain concrete under various loading conditions and especially with considering stress non-equilibrium are reliably reproduced and *** with waveform features,the violation indicator of the specimen stress equilibrium in the split Hopkinson pressure bar test is identified for concrete-like damage softening *** concrete material behaviors for stress non-equilibrium are further analyzed,*** dynamic increase factor(DIF)and damage development,*** conception of“damage failure volume”is introduced,and a new method of defining the development of concrete dynamic damage is given in the nimierical ***’s more,the“compression wave”and“double peak”phenomena observed in the experiment are further interpreted based on the means of numerical *** features how to reflect the concrete material properties is also *** results show that,the disappearance of the“double peak” phenomenon of reflection curve under high strain rate can be regarded as the indicator of the violation of stress *** the violation of the stress equilibrium,the relevant DIFs of the concrete specimen will not change ***,the concrete specimen will turn into structural response from material *** conception of“damage failure volume”can well explain the generation of the“double peak”phenomenon of the reflection *** “compression wave” phenomenon of reflection curve under lower strain rates is derived from the unloading expansion recovery of the concrete ***,under the same loading condition,the amplitude of the first peak of the reflection curve can be used as the evaluation standard of the bonding quality between mortar and aggregates.

关键词： Concrete material Split Hopkinson pressure bar test Numerical investigation Waveform feature Stress non-equilibrium Damage failure volume

STABILITY OF STEADY MULTI-WAVE CONFIgURATIONS FOR THE FULL EULER EQUATIONS OF COMPRESSIBLE FLUID FLOW

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Acta Mathematica Scientia 2018年第5期38卷 1485-1514页

作者： gui-Qiang g.chen Matthew RIgBY Mathematical Institute University of OxfordOxfordOX2 6GGU

We are concerned with the stability of steady multi-wave configurations for the full Euler equations of compressible fluid flow. In this paper, we focus on the stability of steady four-wave configurations that are the solutions of the Riemann problem in the flow direction, consisting of two shocks, one vortex sheet, and one entropy wave, which is one of the core multi-wave configurations for the two-dimensional Euler equations. It is proved that such steady four-wave configurations in supersonic flow are stable in structure globally, even under the BV perturbation of the incoming flow in the flow direction. In order to achieve this, we first formulate the problem as the Cauchy problem （initial value problem） in the flow direction, and then develop a modified glimm difference scheme and identify a glimm-type functional to obtain the required BV estimates by tracing the interactions not only between the strong shocks and weak waves, but also between the strong vortex sheet/entropy wave and weak waves. The key feature of the Euler equations is that the reflection coefficient is always less than 1, when a weak wave of different family interacts with the strong vortex sheet/entropy wave or the shock wave, which is crucial to guarantee that the glimm functional is decreasing. Then these estimates are employed to establish the convergence of the approximate solutions to a global entropy solution, close to the background solution of steady four-wave configuration.

关键词： stability multi-wave configuration vortex sheet entropy wave shock wave BV perturbation full Euler equations steady wave interactions glimm scheme

Invariant Measures for Nonlinear Conservation Laws Driven by Stochastic Forcing

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Chinese Annals of Mathematics,Series B 2019年第6期40卷 967-1004页

作者： gui-Qiang g.chen Peter H.C.PANg Mathematical Institute University of Oxford

Some recent developments in the analysis of long-time behaviors of stochastic solutions of nonlinear conservation laws driven by stochastic forcing are *** existence and uniqueness of invariant measures are established for anisotropic degenerate parabolic-hyperbolic conservation laws of second-order driven by white *** further developments,problems,and challenges in this direction are also discussed.

关键词： Stochastic solutions Entropy solutions Invariant measures Existence Uniqueness Stochastic forcing Anisotropic degenerate Parabolichyperbolic equations Long-time behavior

Reduction-induced metal/oxide interfacial sites for selective CO_(2) hydrogenation

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SmartMat 2023年第4期4卷 199-209页

作者： Zhenhua Xie Sooyeon Hwang Jingguang g.chen Department of Chemical Engineering Columbia UniversityNew YorkNew YorkUSA Chemistry Division Brookhaven National LaboratoryUptonNew YorkUSA Center for Functional Nanomaterials Brookhaven National LaboratoryUptonNew YorkUSA

The interfacial structures of bimetallic-derived catalysts play an important role in promoting the activation of reactants such as CO_(2).In particular,both the physical property(e.g.,local bonding environment)and the electronic property(e.g.,oxidation state)can evolve from their native states under different environments,such as upon reduction and during the catalytic ***,taking the CO_(2) hydrogenation reaction over Rh-based catalysts as a case study,the present work compares the interfacial structures in tuning the selectivity toward CH_(4) or *** combination of ex situ and in situ characterization reveals two representative interfacial structures:the Rh/CeO_(x) interface formed over Rh/CeO_(2) is active and selective to produce CH_(4)(~95%)by following a formate-mediated pathway;in comparison,the InO_(x)/Rh interface derived after reduction is active for CO_(2) activation and enables a redox mechanism for the exclusive formation of CO(~100%).This work provides insights into the environment-induced structural evolution at the metal−oxide interfaces,as well as the role of distinct interfacial active sites in tuning the selectivity of CO_(2) hydrogenation.

关键词： CO_(2) hydrogenation interfacial structure Rh-based catalysts structural evolution

Coupling CO_(2)reduction with ethane aromatization for enhancing catalytic stability of iron-modified ZSM-5

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Journal of Energy Chemistry 2022年第3期31卷 210-217,I0007页

作者： Zhenhua Xie Elaine gomez Dong Wang Ji Hoon Lee Tiefeng Wang Jingguang g.chen Department of Chemical Engineering Columbia UniversityNew YorkNY 10027USA Chemistry Division Brookhaven National LaboratoryUptonNY 11973USA Department of Chemical Engineering Tsinghua UniversityBeijing100084 BeijingChina

The shale gas revolution and the carbon-neutrality goal are motivating the landscape toward the synthesis of value-added chemicals or fuels from underutilized ethane with the assistance of greenhouse gas CO_(2).Combining ethane aromatization with CO_(2)reduction offers an opportunity to directly produce liquid products for facile separation,storage,and *** the present work,Fe/ZSM-5 catalysts showed promise in the simultaneous CO_(2)reduction and ethane aromatization at atmospheric pressure and 873 *** catalysts were further investigated using X-ray diffraction(XRD)and X-ray absorption fine structure(XAFS)measurements under in-situ conditions,indicating that most of Fe species existed in the form of Fe oxides and a portion of Fe was incorporated into the ZSM-5 framework generating Lewis acid *** types of Fe species remained almost unchanged under reaction conditions,contributing to an enhanced aromatization activity of Fe/*** effects of CO_(2)and steam on the acid sites and in turn aromatization activity were also investigated by transient studies,which exhibited a reversible modification ***,CO_(2)was identified to be critical to enhance coke resistance and in turn catalyst *** work highlights the feasibility of using CO_(2)to assist the upgrading of abundant ethane from shale gas to aromatics over non-precious Fe-based zeolite catalysts.

关键词： Ethane CO_(2) Aromatization Fe-modified ZSM-5