Non-negative solutions of generalized porous medium equations.

Bjorn E. J. Dahlberg; Carlos E. Kenig

Revista Matemática Iberoamericana (1986)

  • Volume: 2, Issue: 3, page 267-305
  • ISSN: 0213-2230

Abstract

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The purpose of this paper is to study nonnegative solutions u of the nonlinear evolution equations∂u/∂t = Δφ(u),  x ∈ Rn, 0 < t < T ≤ +∞  (1.1)Here the nonlinearity φ is assumed to be continuous, increasing with φ(0) = 0. This equation arises in various physical problems, and specializing φ leads to models for nonlinear filtrations, or for the gas flow in a porous medium. For a recent survey in these equations see [9].The main object of this work is to study the initial value problem for (1,1).

How to cite

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Dahlberg, Bjorn E. J., and Kenig, Carlos E.. "Non-negative solutions of generalized porous medium equations.." Revista Matemática Iberoamericana 2.3 (1986): 267-305. <http://eudml.org/doc/39328>.

@article{Dahlberg1986,
abstract = {The purpose of this paper is to study nonnegative solutions u of the nonlinear evolution equations∂u/∂t = Δφ(u),  x ∈ Rn, 0 &lt; t &lt; T ≤ +∞  (1.1)Here the nonlinearity φ is assumed to be continuous, increasing with φ(0) = 0. This equation arises in various physical problems, and specializing φ leads to models for nonlinear filtrations, or for the gas flow in a porous medium. For a recent survey in these equations see [9].The main object of this work is to study the initial value problem for (1,1). },
author = {Dahlberg, Bjorn E. J., Kenig, Carlos E.},
journal = {Revista Matemática Iberoamericana},
keywords = {Ecuaciones de evolución no lineales; Valores iniciales; non-negative solutions; nonlinear filtration; trace; non-linearities},
language = {eng},
number = {3},
pages = {267-305},
title = {Non-negative solutions of generalized porous medium equations.},
url = {http://eudml.org/doc/39328},
volume = {2},
year = {1986},
}

TY - JOUR
AU - Dahlberg, Bjorn E. J.
AU - Kenig, Carlos E.
TI - Non-negative solutions of generalized porous medium equations.
JO - Revista Matemática Iberoamericana
PY - 1986
VL - 2
IS - 3
SP - 267
EP - 305
AB - The purpose of this paper is to study nonnegative solutions u of the nonlinear evolution equations∂u/∂t = Δφ(u),  x ∈ Rn, 0 &lt; t &lt; T ≤ +∞  (1.1)Here the nonlinearity φ is assumed to be continuous, increasing with φ(0) = 0. This equation arises in various physical problems, and specializing φ leads to models for nonlinear filtrations, or for the gas flow in a porous medium. For a recent survey in these equations see [9].The main object of this work is to study the initial value problem for (1,1).
LA - eng
KW - Ecuaciones de evolución no lineales; Valores iniciales; non-negative solutions; nonlinear filtration; trace; non-linearities
UR - http://eudml.org/doc/39328
ER -

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