Acta mathematica scientia, Series B >
THE HOMOGENEOUS DIRICHLET PROBLEM FOR QUASILINEAR ANISOTROPIC DEGENERATE PARABOLIC-HYPERBOLIC EQUATION#br# WITH Lp INITIAL VALUE
Received date: 2011-09-19
Online published: 2012-09-20
Supported by
Yachun Li’s research was supported partly by National Natural Science Foundation of China (10571120, 10971135), the Program for New Century Excellent Talents of Chinese Ministry of Education (NCET-07-0546) and Shanghai Shuguang Project 06SG11. ZhigangWang’s research was supported partly by Shanghai Jiao Tong University Innovation Fund For Postgraduates (AE071202), the University Young
Teacher Sciences Foundation of Anhui Province (2010SQRL145) and the Quality Project Found of Fuyang Normal College (2010JPKC07).
The aim of this paper is to prove the well-posedness (existence and uniqueness) of the Lp entropy solution to the homogeneous Dirichlet problems for the anisotropic degenerate parabolic-hyperbolic equations with Lp initial value. We use the device of doubling variables and some technical analysis to prove the uniqueness result. Moreover we can prove that the Lp entropy solution can be obtained as the limit of solutions of the corresponding regularized equations of nondegenerate parabolic type.
WANG Zhi-Gang , LI Ya-Chun . THE HOMOGENEOUS DIRICHLET PROBLEM FOR QUASILINEAR ANISOTROPIC DEGENERATE PARABOLIC-HYPERBOLIC EQUATION#br# WITH Lp INITIAL VALUE[J]. Acta mathematica scientia, Series B, 2012 , 32(5) : 1727 -1742 . DOI: 10.1016/S0252-9602(12)60137-4
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