VERY WEAK SOLUTIONS OF SINGULAR POROUS MEDIUM EQUATIONS WITH MEASURE DATA

Bögelein V, Duzaar F, Gianazza U (2015)

Publication Status: Published

Publication Type: Journal article

Publication year: 2015

Journal

Communications on Pure and Applied Analysis American Institute of Mathematical Sciences (AIMS)

Publisher: American Institute of Mathematical Sciences (AIMS)

Book Volume: 14

Pages Range: 23-49

Journal Issue: 1

DOI: 10.3934/cpaa.2015.14.23

Abstract

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.

Authors with CRIS profile

Frank Duzaar Lehrstuhl für Partial Differential Equations

Involved external institutions

Universität Salzburg (Paris Lodron Universität Salzburg) AT Austria (AT) Università degli Studi di Pavia IT Italy (IT)

How to cite

APA:

Bögelein, V., Duzaar, F., & Gianazza, U. (2015). VERY WEAK SOLUTIONS OF SINGULAR POROUS MEDIUM EQUATIONS WITH MEASURE DATA. Communications on Pure and Applied Analysis, 14(1), 23-49. https://doi.org/10.3934/cpaa.2015.14.23

MLA:

Bögelein, Verena, Frank Duzaar, and Ugo Gianazza. "VERY WEAK SOLUTIONS OF SINGULAR POROUS MEDIUM EQUATIONS WITH MEASURE DATA." Communications on Pure and Applied Analysis 14.1 (2015): 23-49.

BibTeX: Download