Nonlinear Elliptic-Parabolic Problems

被引：9
作者：
Kim, Inwon C. [1 ]
Pozar, Norbert [2 ]
机构：
[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA
[2] Univ Tokyo, Grad Sch Math Sci, Meguro Ku, Tokyo 1538914, Japan
来源：
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2013年 / 210卷 / 03期
基金：
日本学术振兴会;
关键词：
FREE-BOUNDARY PROBLEM; VISCOSITY SOLUTIONS; DIFFERENTIAL-EQUATIONS; REGULARITY THEORY; POROUS-MEDIA; UNIQUENESS;
D O I：
10.1007/s00205-013-0663-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We introduce a notion of viscosity solutions for a general class of elliptic-parabolic phase transition problems. These include the Richards equation, which is a classical model in filtration theory. Existence and uniqueness results are proved via the comparison principle. In particular, we show existence and stability properties of maximal and minimal viscosity solutions for a general class of initial data. These results are new, even in the linear case, where we also show that viscosity solutions coincide with the regular weak solutions introduced in Alt and Luckhaus (Math Z 183:311-341, 1983).
引用
收藏
页码：975 / 1020
页数：46
相关论文
共 28 条
  • [1] ALT HW, 1983, MATH Z, V183, P311
  • [2] [Anonymous], 2005, A geometric approach to free boundary problems
  • [3] [Anonymous], 2010, GRADUATE STUDIES MAT
  • [4] [Anonymous], 2007, POROUS MEDIUM EQUATI
  • [5] [Anonymous], 1967, Linear and Quasilinear Equations of Parabolic Type
  • [6] [Anonymous], 1995, Fully nonlinear elliptic equations
  • [7] ARMSTRONG S., THESIS
  • [8] REGULARITY RESULTS FOR AN ELLIPTIC-PARABOLIC FREE-BOUNDARY PROBLEM
    BERTSCH, M
    HULSHOF, J
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1986, 297 (01) : 337 - 350
  • [9] Brändle C, 2005, INDIANA U MATH J, V54, P817
  • [10] Cararelli L A, 1999, P S PUR MATH, V65, P13
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