On certain nonlinear parabolic equations with singular diffusion and data in L1

被引：5
作者：
Vázquez, CG [1 ]
Gallego, FO [1 ]
机构：
[1] Univ Cadiz, Dept Matemat, CASEM, Cadiz, Spain
来源：
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2005年 / 4卷 / 03期
关键词：
nonlinear parabolic equations; singular diffusion; renormalized solutions; Sobolev spaces;
D O I：
10.3934/cpaa.2005.4.589
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
An existence result is established for a class of nonlinear parabolic equations having a coercive diffusion matrix blowing-up for a finite value of the unknown, a second hand f is an element of L-1(Q), and an initial data u(o) is an element of L-1(Omega). We develop a technique which relies on the notion of a renormalized solution and an adequate regularization in time for certain truncation functions. Some uniqueness results are also shown under additional hypotheses.
引用
收藏
页码：589 / 612
页数：24
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