Articles

EXISTENCE AND UNIQUENESS OF RENORMALIZED SOLUTIONS FOR A CLASS OF DEGENERATE PARABOLIC EQUATIONS

  • ZHANG Li-Qin ,
  • DIAO Dun-Ning
Expand
  • Department of Mathematics, Xiamen University of Technology, Xiamen 361005, China Department of Mathematics, Xiamen University, Xiamen 361005, China

Received date: 2006-06-22

  Revised date: 2006-11-01

  Online published: 2009-03-20

Supported by

Partially supported by Science Foundation of Xiamen University of Technology (YKJ08020R)

Abstract

This article discusses the existence and uniqueness of renormalized solutions for a class of degenerate parabolic equations b(u)t − div(a(u,∇u)) = H(u)(f + divg).

Cite this article

ZHANG Li-Qin , DIAO Dun-Ning . EXISTENCE AND UNIQUENESS OF RENORMALIZED SOLUTIONS FOR A CLASS OF DEGENERATE PARABOLIC EQUATIONS[J]. Acta mathematica scientia, Series B, 2009 , 29(2) : 251 -264 . DOI: 10.1016/S0252-9602(09)60026-6

References


[1] DiPerna R J, Lions P L. On the Cauchy problem for Boltzmann equations: Global existence and weak
stability. Ann Math, 1989, 130: 321–366


[2] Lions P L. Mathematical topics in fluids mechanics, incompressible models. New York: Oxford Univ Press,
1996, 1: 11–208


[3] Amma K, Wittbold P. Existence of renormalized solutions of degenerate elliptic-parabolic problems. Pro-
ceedings of the Royal Society of Edinburgh, 2003, 133A: 477–496


[4] Carrillo J, Wittbold P. Uniqueness of renormalized solutions of degenerate elliptic-parabolic problems. J
Diff Equ, 1999, 156: 93–121


[5] Dominique Blanchard, Francois Murat, Hicham Redwane. Existence and uniqueness of a renormalized
solution for a fairly general class nonlinear parabolic problems. J Diff Equ, 2001, 177: 331–374


[6] Francois Murat, Porretta A. Stability properties, existence and nonexistence of renormalized solutions for
elliptic equations with measure data. Comm P D E, 2002, 27(11/12): 2267–2310


[7] Boccardo L, Giachetti D, Diaz J I, Murat F. Existence and regularity of renormalized solutions for some
elliptic problems involving derivations of nonlinear terms. J Diff Equ, 1993, 106: 215–237


[8] Simon J. Compact sets in Lp(0, T;B). Ann Mat Pura Appl, 1987, 146(4): 65–96


[9] Landes R. On the existence of weak solutions for quasilinear parabolic initial boundary-value problems.
Proc T Soc Edinb, 1981, 89A: 217–237


[10] Boccardo L, Murat F, Puel J P. Existence of bounded solutions for nonlinear elliptic unilateral problems.
Ann Mat Pura Appl, 1988, 152: 183–196

Outlines

/