Very weak solutions of singular porous medium equations with measure data | Zendy

Ugo Gianazza | Zendy; Frank Duzaar | Zendy; Verena Bögelein | Zendy

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Very weak solutions of singular porous medium equations with measure data

Author(s) -

Ugo Gianazza,

Frank Duzaar,

Verena Bögelein

Publication year - 2014

Publication title -

communications on pure andamp applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.077

H-Index - 42

eISSN - 1553-5258

pISSN - 1534-0392

DOI - 10.3934/cpaa.2015.14.23

Subject(s) - pointwise , mathematical analysis , measure (data warehouse) , dirichlet boundary condition , mathematics , porous medium , homogeneous , domain (mathematical analysis) , radon measure , cauchy distribution , boundary value problem , type (biology) , weak solution , cauchy boundary condition , singular solution , porosity , pure mathematics , combinatorics , materials science , locally compact space , ecology , database , computer science , composite material , biology

We consider non-homogeneous, singular ($ 0 < m < 1 $) porous medium type equations with a non-negative Radon-measure $\mu$ 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.

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