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Dive into the research topics where Yunguang Lu is active.

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Featured researches published by Yunguang Lu.


Applied Mathematics Letters | 2000

Hölder estimates of solutions of biological population equations

Yunguang Lu

In this paper, the Cauchy problem of the degenerate parabolic equations (1) arisen in the spread of biological populations is studied. Holder continuous solutions u with exponents 23 with respect to the variables x, y and 14 with respect to t are obtained.


Acta Mathematica Scientia | 1992

CONVERGENCE OF THE VISCOSITY METHOD FOR A NONSTRICTLY HYPERBOLIC SYSTEM

Yunguang Lu

A convergence theorem for the viscosity method applied to the following nonstrictly hyperbolic system is established. Convergence of a subsequence in the strong topology is proved without uniform estimates on the derivatives, by using the theory of compensated compactness and an analysis of progressing entrory waves.


Proceedings of the American Mathematical Society | 2002

Regularity of viscosity solutions of a degenerate parabolic equation

L. Qian; Yunguang Lu

We study the Cauchy problem for the nonlinear degenerate parabolic equation of second order {u t = uΔu - γ|⊇u| 2 in Ω = R N × R + , u(x,0) = u 0 (x) in R N , and present regularity results for the viscosity solutions.


Applied Mathematics Letters | 2006

Global weak solution for a symmetrically hyperbolic system

Yunguang Lu

In this work, the existence of bounded weak solutions is obtained for the Cauchy problem of a symmetrically hyperbolic system, arising in such areas as elasticity theory, magnetohydrodynamics, and enhanced oil recovery.


Advanced Nonlinear Studies | 2001

Convergence of Approximated Solutions to a Nonstrictly Hyperbolic System

Yunguang Lu; Ignacio Mantilla; Leonardo Rendón

Abstract In this paper, four classes of special entropy-entropy flux pairs of Lax type for the nonstrictly hyperbolic system of type (1.1) (Le Roux system) are constructed based on the solutions of the standard Fuchsion equation. The second derivatives of these entropies are all singular at the point (0,O). A careful computation for these entropies at the singular point shows the compactness of η(u1, v1)t + q(u1, v1)x in H-1loc:(R x R+) with respect to the approximated solutions constructed by using viscosity method or Friedrichs-Lax scheme method. These entropies provide a convergence theorem in the strong topology for the artifical viscosity method or Friedrichs-Lax scheme method when applied to the Cauchy problem (1.1),(1.4) and used together with the theory of compensated compactness.


Acta Mathematica Scientia | 1990

CONVERGENCE OF THE APPROXIMATE SOLUTIONS TO ISENTROPIC GAS DYNAMICS

Guiqiang Ohen; Yunguang Lu

Abstract This paper gives four pairs of entropies (ηi, qj) (i=1, 2, 3, 4) to the isentropic gas dynamics equations { ρ t + ( ρ u ) x = 0 ( ρ u ) t + ( ρ u 2 + p ( ρ ) ) x = 0 p ( ρ ) = k 2 ρ γ , 1 γ 3. } when all the function equations are satisfied 〈 v , η i q j - η j q i 〉 = 〈 v , η i 〉 〈 v , q j 〉 - 〈 v , η j 〉 〈 v , q i 〉 . where supp v is small, v is a Dirac mass under a strong confine ρ ≥ C ( T ) > 0 .


Abstract and Applied Analysis | 2014

Global Solutions for a Simplified Shallow Elastic Fluids Model

Yunguang Lu; Christian Klingenberg; Leonardo Rendón; Deyin Zheng

The Cauchy problem for a simplified shallow elastic fluids model, one system of Temple’s type, is studied and a global weak solution is obtained by using the compensated compactness theorem coupled with the total variation estimates on the first and third Riemann invariants, where the second Riemann invariant is singular near the zero layer depth . This work extends in some sense the previous works, (Serre, 1987) and (Leveque and Temple, 1985), which provided the global existence of weak solutions for strictly hyperbolic system and (Heibig, 1994) for strictly hyperbolic system with smooth Riemann invariants.


Acta Mathematica Scientia | 1988

THE ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF INITIAL VALUE PROBLEM TO SYSTEM OF GAS DYNAMICS WITH VISCOSITY

Yunguang Lu; Guiliang Xie

Abstract This paper considers the system (A) { υ t - u x = ɛ υ x x u t + p ( υ ) x = ɛ u x x , x ∈ R , t > 0 where p ( υ ) = a υ - r , a > 0 , r > 1 , with (B) ( υ ( x , 0 ) , u ( x , 0 ) ) = ( υ 0 ( x ) , u 0 ( x ) ) , x ∈ R where x → ± ∞ lim ( υ 0 ( x ) , u 0 ( x ) ) = ( υ ± , u ± ) provided (C1) 0 υ - υ + , u + u - (C2) 0 υ + υ - , u + u - or (C3) 0 υ + υ - , u - u + (C4) 0 υ - υ + , u - u + The traveling wave solution of problem (A), (B) is proved to be asymptotically stable when (C)1, (C)2 are satisfied and rarefaction wave solution is proved to be asymptotical when (C)3, (C)4 are satisfied, provided that the initial disturbance is suitably small and of zero constant component. The proof is given by the elemental L2 energy method.


Nonlinear Analysis-theory Methods & Applications | 1993

Viscous solutions of quadratic conservation laws with umbilic points

Yunguang Lu; Changjiang Zhu; Huijiang Zhao

VISCOUS SOLUTIONS OF QUADRATIC CONSERVATION LAWS WITH UMBILIC POINTS LTJ YUNGUANG, ZHU CHANGJIANG and ZHAO HUIJIANG Wuhan Institute of Mathematical Sciences, Academia Sinica, Wuhan, 430071, People’s Republic of China (Received 10 January 1991; received in revised form 4 August 1992; received for publication 1 March 1993)


Acta Mathematica Scientia | 1992

EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTION TO INHOMOGENEOUS SYSTEMS OF GAS DYNAMICS WITH VISCOSITY

Yunguang Lu

Abstract This paper considers the existence and asymptotic behaviors of the solutions to the inhomogeneous systems of gas dynamics with viscosity:

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Leonardo Rendón

National University of Colombia

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Ignacio Mantilla

National University of Colombia

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Changjiang Zhu

Central China Normal University

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Guiliang Xie

Central China Normal University

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Huijiang Zhao

Chinese Academy of Sciences

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Jose Francisco Caicedo

University of Science and Technology of China

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Yue-Jun Peng

Blaise Pascal University

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