Yunguang Lu
National University of Colombia
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Featured researches published by Yunguang Lu.
Applied Mathematics Letters | 2000
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
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
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
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
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
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
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
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
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
Yunguang Lu
Abstract This paper considers the existence and asymptotic behaviors of the solutions to the inhomogeneous systems of gas dynamics with viscosity: