Yuxi Zheng

  • Department Head and Francis R. Pentz and Helen M. Pentz Professor of Science, Mathematics
    • 1960 Citations
    • 30 h-Index
    1989 …2020
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    Research Output 1989 2020

    • 1960 Citations
    • 30 h-Index
    • 61 Article
    • 1 Chapter
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    Article
    2020

    The Riemann problem for a blood flow model in arteries

    Sheng, W., Zhang, Q. & Zheng, Y., Jan 1 2020, In : Communications in Computational Physics. 27, 1, p. 227-250 24 p.

    Research output: Contribution to journalArticle

    Open Access
    Cauchy problem
    blood flow
    arteries
    uniqueness
    elastic waves
    2016

    No blow-up to a variational wave equation in liquid crystals

    Huang, J. & Zheng, Y., Feb 1 2016, In : Journal of Mathematical Physics. 57, 2, 021506.

    Research output: Contribution to journalArticle

    Variational Equation
    Cauchy problem
    Nematic Liquid Crystal
    Smooth Solution
    Liquid Crystal
    7 Citations (Scopus)

    The structure of solutions near a sonic line in gas dynamics via the pressure gradient equation

    Zhang, T. & Zheng, Y., Nov 1 2016, In : Journal of Mathematical Analysis and Applications. 443, 1, p. 39-56 18 p.

    Research output: Contribution to journalArticle

    Gas dynamics
    Gas Dynamics
    Pressure Gradient
    Pressure gradient
    Boundary conditions
    2015
    12 Citations (Scopus)

    The regularity of semihyperbolic patches near sonic lines for the 2-d euler system in gas dynamics

    Song, K., Wang, Q. & Zheng, Y., Jan 1 2015, In : SIAM Journal on Mathematical Analysis. 47, 3, p. 2200-2219 20 p.

    Research output: Contribution to journalArticle

    Euler System
    2-D Systems
    Gas dynamics
    Gas Dynamics
    Patch
    2014
    12 Citations (Scopus)

    Sonic-supersonic solutions for the steady Euler equations

    Zhang, T. & Zheng, Y., Jan 1 2014, In : Indiana University Mathematics Journal. 63, 6, p. 1785-1817 33 p.

    Research output: Contribution to journalArticle

    Euler Equations
    Curve
    Shock
    Euler System
    Transonic Flow
    11 Citations (Scopus)
    Gas Dynamics
    Pressure Gradient
    Patch
    Regularity
    Line
    2013
    5 Citations (Scopus)

    Characteristic decouplings and interactions of rarefaction waves of 2D Euler equations

    Ji, X. & Zheng, Y., Oct 1 2013, In : Journal of Mathematical Analysis and Applications. 406, 1, p. 4-14 11 p.

    Research output: Contribution to journalArticle

    Rarefaction Wave
    Euler equations
    Decoupling
    Euler Equations
    Decomposition
    10 Citations (Scopus)

    Energy conservative solutions to a nonlinear wave system of nematic liquid crystals

    Chen, G., Zhang, P. & Zheng, Y., May 1 2013, In : Communications on Pure and Applied Analysis. 12, 3, p. 1445-1468 24 p.

    Research output: Contribution to journalArticle

    Nematic liquid crystals
    Nonlinear Waves
    Nematic Liquid Crystal
    Partial differential equations
    Angle
    7 Citations (Scopus)

    Singularity and existence for a wave system of nematic liquid crystals

    Chen, G. & Zheng, Y., Feb 1 2013, In : Journal of Mathematical Analysis and Applications. 398, 1, p. 170-188 19 p.

    Research output: Contribution to journalArticle

    Damping Term
    Nematic liquid crystals
    Nematic Liquid Crystal
    System Modeling
    Global Existence
    2012
    19 Citations (Scopus)

    Energy conservative solutions to a one-dimensional full variational wave system

    Zhang, P. & Zheng, Y., May 1 2012, In : Communications on Pure and Applied Mathematics. 65, 5, p. 683-726 44 p.

    Research output: Contribution to journalArticle

    Initial value problems
    Wave equations
    Liquid crystals
    Energy
    Variational Equation
    9 Citations (Scopus)

    Local existence of classical solutions to shallow water equations with Cauchy data containing vacuum

    Duan, B., Luo, Z. & Zheng, Y., May 28 2012, In : SIAM Journal on Mathematical Analysis. 44, 2, p. 541-567 27 p.

    Research output: Contribution to journalArticle

    Local Existence
    Shallow Water Equations
    Classical Solution
    Cauchy
    Vacuum
    2011
    45 Citations (Scopus)

    Characteristic decompositions and interactions of rarefaction waves of 2-D Euler equations

    Li, J., Yang, Z. & Zheng, Y., Jan 15 2011, In : Journal of Differential Equations. 250, 2, p. 782-798 17 p.

    Research output: Contribution to journalArticle

    Rarefaction Wave
    Euler equations
    Euler Equations
    Decomposition
    Decompose
    39 Citations (Scopus)

    Semi-hyperbolic Patches of Solutions to the Two-dimensional Euler Equations

    Li, M. & Zheng, Y., Sep 1 2011, In : Archive for Rational Mechanics and Analysis. 201, 3, p. 1069-1096 28 p.

    Research output: Contribution to journalArticle

    Euler equations
    Euler Equations
    Patch
    Transonic Flow
    Transonic flow
    33 Citations (Scopus)

    Simple waves and pressure delta waves for a Chaplygin gas in two-dimensions

    Lai, G., Sheng, W. & Zheng, Y., Oct 1 2011, In : Discrete and Continuous Dynamical Systems. 31, 2, p. 489-523 35 p.

    Research output: Contribution to journalArticle

    Chaplygin Gas
    Two Dimensions
    Gases
    Discontinuity
    Cauchy Problem
    2010
    21 Citations (Scopus)

    Conservative solutions to a system of variational wave equations of nematic liquid crystals

    Zhang, P. & Zheng, Y., Mar 1 2010, In : Archive for Rational Mechanics and Analysis. 195, 3, p. 701-727 27 p.

    Research output: Contribution to journalArticle

    Variational Equation
    Nematic liquid crystals
    Nematic Liquid Crystal
    Wave equations
    Hyperbolic Equations
    46 Citations (Scopus)

    Interaction of four rarefaction waves in the bi-symmetric class of the two-dimensional euler equations

    Li, J. & Zheng, Y., Mar 8 2010, In : Communications In Mathematical Physics. 296, 2, p. 303-321 19 p.

    Research output: Contribution to journalArticle

    Rarefaction Wave
    Euler Equations
    elastic waves
    Interaction
    hodographs
    39 Citations (Scopus)

    The interaction of rarefaction waves of the two-dimensional euler equations

    Chen, X. & Zheng, Y., Jul 20 2010, In : Indiana University Mathematics Journal. 59, 1, p. 231-256 26 p.

    Research output: Contribution to journalArticle

    Rarefaction Wave
    Euler Equations
    Self-similar Solutions
    Interaction
    Angle
    2009
    13 Citations (Scopus)

    Absorption of characteristics by sonic curve of the two-dimensional euler equations

    Zheng, Y., Jan 1 2009, In : Discrete and Continuous Dynamical Systems. 23, 1-2, p. 605-616 12 p.

    Research output: Contribution to journalArticle

    Euler equations
    Euler Equations
    Boundary value problems
    Absorption
    Determinacy
    66 Citations (Scopus)

    Interaction of rarefaction waves of the two-dimensional self-similar Euler equations

    Li, J. & Zheng, Y., Jul 1 2009, In : Archive for Rational Mechanics and Analysis. 193, 3, p. 623-657 35 p.

    Research output: Contribution to journalArticle

    Rarefaction Wave
    Euler equations
    Euler Equations
    Vacuum
    Gases
    40 Citations (Scopus)

    Semi-hyperbolic patches of solutions of the pressure gradient system

    Song, K. & Zheng, Y., Aug 1 2009, In : Discrete and Continuous Dynamical Systems. 24, 4, p. 1365-1380 16 p.

    Research output: Contribution to journalArticle

    Gradient System
    Pressure Gradient
    Pressure gradient
    Patch
    Tile
    21 Citations (Scopus)

    Two-dimensional Riemann problems: from scalar conservation laws to compressible Euler equations

    Jiequan, L., Wancheng, S., Tong, Z. & Zheng, Y., Jul 1 2009, In : Acta Mathematica Scientia. 29, 4, p. 777-802 26 p.

    Research output: Contribution to journalArticle

    Compressible Euler Equations
    Cauchy problem
    Scalar Conservation Laws
    Hyperbolic Conservation Laws
    Gas Dynamics
    1 Citation (Scopus)

    Two-dimensional Riemann problems for the compressible Euler system

    Zheng, Y., Dec 1 2009, In : Chinese Annals of Mathematics. Series B. 30, 6, p. 845-858 14 p.

    Research output: Contribution to journalArticle

    Euler System
    Cauchy Problem
    Computer simulation
    Asymptotic analysis
    Numerical Simulation
    2008
    38 Citations (Scopus)

    Transonic shock formation in a rarefaction riemann problem for the 2D compressible euler equations

    Glimm, J., Li, X., Li, J., Li, X., Zhang, P., Zhang, T. & Zheng, Y., Dec 1 2008, In : SIAM Journal on Applied Mathematics. 69, 3, p. 720-742 23 p.

    Research output: Contribution to journalArticle

    Compressible Euler Equations
    Euler equations
    Shock Waves
    Shock
    Rarefaction Wave
    2007
    21 Citations (Scopus)

    A complete global solution to the pressure gradient equation

    Lei, Z. & Zheng, Y., May 1 2007, In : Journal of Differential Equations. 236, 1, p. 280-292 13 p.

    Research output: Contribution to journalArticle

    Pressure Gradient
    Pressure gradient
    Global Solution
    Vacuum
    Quadrant
    32 Citations (Scopus)

    Asymptotic variational wave equations

    Bressan, A., Zhang, P. & Zheng, Y., Jan 1 2007, In : Archive for Rational Mechanics and Analysis. 183, 1, p. 163-185 23 p.

    Research output: Contribution to journalArticle

    Variational Equation
    Wave equations
    Wave equation
    Cauchy Problem
    Energy
    2006
    41 Citations (Scopus)

    Conservative solutions to a nonlinear variational wave equation

    Bressan, A. & Zheng, Y., Sep 1 2006, In : Communications In Mathematical Physics. 266, 2, p. 471-497 27 p.

    Research output: Contribution to journalArticle

    Variational Equation
    Cauchy problem
    Smooth function
    wave equations
    Weak Solution
    18 Citations (Scopus)

    Numerical evidence of nonuniqueness in the evolution of vortex sheets

    Lopes Filho, M. C., Lowengrub, J., Nussenzveig Lopes, H. J. & Zheng, Y., Jun 29 2006, In : Mathematical Modelling and Numerical Analysis. 40, 2, p. 225-237 13 p.

    Research output: Contribution to journalArticle

    Vortex Sheet
    Nonuniqueness
    Vorticity
    Weak Solution
    Vortex flow
    66 Citations (Scopus)

    Simple waves and a characteristic decomposition of the two dimensional compressible euler equations

    Li, J., Zhang, T. & Zheng, Y., Oct 1 2006, In : Communications In Mathematical Physics. 267, 1, p. 1-12 12 p.

    Research output: Contribution to journalArticle

    Compressible Euler Equations
    potential flow
    Potential Flow
    decomposition
    Decompose
    63 Citations (Scopus)

    Two-dimensional regular shock reflection for the pressure gradient system of conservation laws

    Zheng, Y., Apr 1 2006, In : Acta Mathematicae Applicatae Sinica. 22, 2, p. 177-210 34 p.

    Research output: Contribution to journalArticle

    Gradient System
    Systems of Conservation Laws
    Pressure Gradient
    Pressure gradient
    Euler System
    2005
    37 Citations (Scopus)

    Weak solutions to a nonlinear variational wave equation with general data

    Zhang, P. & Zheng, Y., Jan 1 2005, In : Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire. 22, 2, p. 207-226 20 p.

    Research output: Contribution to journalArticle

    Variational Equation
    Wave equations
    Weak Solution
    Wave equation
    Young Measures
    2004
    65 Citations (Scopus)

    Effect of solutes on dislocation motion - A phase-field simulation

    Hu, S. Y., Li, Y. L., Zheng, Y. & Chen, L., Mar 1 2004, In : International journal of plasticity. 20, 3, p. 403-425 23 p.

    Research output: Contribution to journalArticle

    Burgers vector
    Dislocations (crystals)
    Drag
    Solid solutions
    Defects
    2 Citations (Scopus)

    Transient analysis of Linear birth-death processes with immigration and emigration

    Zheng, Y., Chao, X. & Xiaomei, J. I., May 7 2004, In : Probability in the Engineering and Informational Sciences. 18, 2, p. 141-159 19 p.

    Research output: Contribution to journalArticle

    Birth-death Process
    Transient Analysis
    Immigration
    Linear Process
    Transient analysis
    2003
    40 Citations (Scopus)

    A global solution to a two-dimensional Riemann problem involving shocks as free boundaries

    Zheng, Y., Jan 1 2003, In : Acta Mathematicae Applicatae Sinica. 19, 4, p. 559-572 14 p.

    Research output: Contribution to journalArticle

    Shock problems
    Free Boundary
    Shock Waves
    Global Solution
    Shock waves
    28 Citations (Scopus)

    Transient analysis of immigration birth-death processes with total catastrophes

    Chao, X. & Zheng, Y., Jan 1 2003, In : Probability in the Engineering and Informational Sciences. 17, 1, p. 83-106 24 p.

    Research output: Contribution to journalArticle

    Birth-death Process
    Transient Analysis
    Immigration
    Catastrophe
    Transient analysis
    37 Citations (Scopus)

    Weak solutions to a nonlinear variational wave equation

    Zhang, P. & Zheng, Y., Mar 1 2003, In : Archive for Rational Mechanics and Analysis. 166, 4, p. 303-319 17 p.

    Research output: Contribution to journalArticle

    Variational Equation
    Wave equations
    Weak Solution
    Wave equation
    Young Measures
    2002
    12 Citations (Scopus)

    On the second-order asymptotic equation of a variational wave equation

    Zhang, P. & Zheng, Y., Dec 1 2002, In : Royal Society of Edinburgh - Proceedings A. 132, 2, p. 483-509 27 p.

    Research output: Contribution to journalArticle

    Second-order Asymptotics
    Variational Equation
    Wave equation
    Wave Speed
    Annihilation
    32 Citations (Scopus)

    The Limit from the Schrödinger-Poisson to the Vlasov-Poisson Equations with General Data in One Dimension

    Zhang, P., Zheng, Y. & Mauser, N. J., May 1 2002, In : Communications on Pure and Applied Mathematics. 55, 5, p. 582-632 51 p.

    Research output: Contribution to journalArticle

    Vlasov-Poisson Equations
    Poisson equation
    Schrödinger
    One Dimension
    Siméon Denis Poisson
    2001
    33 Citations (Scopus)

    Rarefactive solutions to a nonlinear variational wave equation of liquid crystals

    Zhang, P. & Zheng, Y., Jan 1 2001, In : Communications in Partial Differential Equations. 26, 3-4, p. 381-419 39 p.

    Research output: Contribution to journalArticle

    Variational Equation
    Wave equations
    Liquid Crystal
    Liquid crystals
    Wave equation
    27 Citations (Scopus)

    Singular and rarefactive solutions to a nonlinear variational wave equation

    Zhang, P. & Yuxi, Z., Jan 1 2001, In : Chinese Annals of Mathematics. Series B. 22, 2, p. 159-170 12 p., 0252-9599(2001)02-0159-12.

    Research output: Contribution to journalArticle

    Variational Equation
    Wave equations
    Partial differential equations
    Wave equation
    Singularity
    2000
    52 Citations (Scopus)
    Variational Equation
    Wave equations
    Existence and Uniqueness of Solutions
    Wave equation
    Young Measures
    1999
    4 Citations (Scopus)

    Convergence of the vanishing viscosity approximation for superpositions of confined eddies

    Lopes Filho, M. C., Nussenzveig Lopes, H. J. & Zheng, Y., Jan 1 1999, In : Communications In Mathematical Physics. 201, 2, p. 291-304 14 p.

    Research output: Contribution to journalArticle

    Viscosity Approximation
    Vanishing Viscosity
    Superposition
    Weak Solution
    vortices
    30 Citations (Scopus)

    On the Existence and Uniqueness of Solutions to an Asymptotic Equation of a Variational Wave Equation

    Zhang, P. & Zheng, Y., Dec 1 1999, In : Acta Mathematica Sinica, English Series. 15, 1, p. 115-130 16 p.

    Research output: Contribution to journalArticle

    Variational Equation
    Wave equations
    Existence and Uniqueness of Solutions
    Global Existence
    Weak Solution
    1998
    20 Citations (Scopus)

    Axisymmetric solutions of the Euler equations for polytropic gases

    Zhang, T. & Zheng, Y., Jul 16 1998, In : Archive for Rational Mechanics and Analysis. 142, 3, p. 253-279 27 p.

    Research output: Contribution to journalArticle

    Axisymmetry
    Euler equations
    Euler Equations
    Hurricanes
    Self-similarity
    40 Citations (Scopus)

    On oscillations of an asymptotic equation of a nonlinear variational wave equation

    Zhang, P. & Zheng, Y., Dec 1 1998, In : Asymptotic Analysis. 18, 3-4, p. 307-327 21 p.

    Research output: Contribution to journalArticle

    Variational Equation
    Wave equation
    Oscillation
    Weak Solution
    Regularity
    1997
    26 Citations (Scopus)

    Exact spiral solutions of the two-dimensional Euler equations

    Zhang, T. & Zheng, Y., Dec 1 1997, In : Discrete and Continuous Dynamical Systems. 3, 1, p. 117-133 17 p.

    Research output: Contribution to journalArticle

    Euler equations
    Euler Equations
    Exact Solution
    Axisymmetry
    Numerical Solution
    42 Citations (Scopus)
    Gradient System
    Compressible Euler Equations
    Euler equations
    Pressure Gradient
    Pressure gradient
    1996
    1 Citation (Scopus)

    Explicit and exact swirling solutions of the 2-D Euler equations

    Zhang, T. & Zheng, Y., Dec 1 1996, In : ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik. 76, SUPPL. 2, p. 145-147 3 p.

    Research output: Contribution to journalArticle

    Euler equations
    Euler Equations
    Incompressible Euler Equations
    Anticlockwise
    Clockwise
    50 Citations (Scopus)

    Singularities of a variational wave equation

    Glassey, R. T., Hunter, J. K. & Zheng, Y., Jul 20 1996, In : Journal of Differential Equations. 129, 1, p. 49-78 30 p.

    Research output: Contribution to journalArticle

    Variational Equation
    Wave equations
    Wave equation
    Singularity
    Nematic liquid crystals
    14 Citations (Scopus)

    Steady states of the Vlasov-Poisson-Fokker-Planck system

    Glassey, R., Schaeffer, J. & Zheng, Y., Sep 15 1996, In : Journal of Mathematical Analysis and Applications. 202, 3, p. 1058-1075 18 p.

    Research output: Contribution to journalArticle

    Fokker-Planck
    Nonlinear Elliptic Equations
    Integral equations
    Siméon Denis Poisson
    Integral-differential Equation

    Vlasov-poisson systems with measures as initial data

    Zheng, Y., Dec 1 1996, In : ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik. 76, SUPPL. 2, p. 109-112 4 p.

    Research output: Contribution to journalArticle

    Vlasov-Poisson System
    Weak Solution
    Fokker-Planck
    Vortex Sheet
    Cauchy Problem