VERY WEAK SOLUTIONS OF SINGULAR POROUS MEDIUM EQUATIONS WITH MEASURE DATA

被引：9

作者：

Boegelein, Verena ^{[1
]}

Duzaar, Frank ^{[1
]}

Gianazza, Ugo ^{[2
]}

机构：

[1] Univ Erlangen Nurnberg, Dept Math, D-91056 Erlangen, Germany

[2] Univ Pavia, Dept Math F Casorati, I-27100 Pavia, Italy

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2015年 / 14卷 / 01期

关键词：

Singular porous medium equations; very weak solutions; existence; Riesz potential; boundedness; NONLINEAR PARABOLIC EQUATIONS; ELLIPTIC-EQUATIONS; SUPERSOLUTIONS; GROWTH;

D O I：

10.3934/cpaa.2015.14.23

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider non-homogeneous, singular (0 < m < 1) porous medium type equations with a non-negative Radon-measure it having finite total mass mu(E-T) on the right-hand side. We deal with a Cauchy-Dirichlet problem for these type of equations, with homogeneous boundary conditions on the parabolic boundary of the domain E-T, and we establish the existence of a solution in the sense of distributions. Finally, we show that the constructed solution satisfies linear pointwise estimates via linear Riesz potentials.

引用

页码：23 / 49

页数：27

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