Stochastic dynamic model for porous media equation describing underground resources

N. U. Ahmed, S. Kerbal

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We consider a stochastic model for porous media flow. This is a degenerate nonlinear stochastic parabolic partial differential equation which may change type from parabolic to elliptic and vice versa. We present existence and regularity of weak solutions. We formulate certain control problems for aquifers (under ground water reservoirs) and discuss some open problems.

Original languageEnglish
Pages (from-to)271-286
Number of pages16
JournalCommunications in Applied Analysis
Volume13
Issue number2
Publication statusPublished - Apr 2009

Fingerprint

Porous Media Flow
Porous Medium Equation
Stochastic Partial Differential Equations
Parabolic Partial Differential Equations
Ground Water
Stochastic Dynamics
Stochastic models
Aquifers
Partial differential equations
Weak Solution
Stochastic Model
Porous materials
Groundwater
Dynamic models
Control Problem
Open Problems
Dynamic Model
Regularity
Resources

Keywords

  • Aquifers
  • Nonlinear stochastic partial differential equations
  • Optimal feedback control laws
  • Porous media equations
  • Stochastic models

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Modelling and Simulation
  • Numerical Analysis

Cite this

Stochastic dynamic model for porous media equation describing underground resources. / Ahmed, N. U.; Kerbal, S.

In: Communications in Applied Analysis, Vol. 13, No. 2, 04.2009, p. 271-286.

Research output: Contribution to journalArticle

@article{c04b1dfc489947289622ea724856c68b,
title = "Stochastic dynamic model for porous media equation describing underground resources",
abstract = "We consider a stochastic model for porous media flow. This is a degenerate nonlinear stochastic parabolic partial differential equation which may change type from parabolic to elliptic and vice versa. We present existence and regularity of weak solutions. We formulate certain control problems for aquifers (under ground water reservoirs) and discuss some open problems.",
keywords = "Aquifers, Nonlinear stochastic partial differential equations, Optimal feedback control laws, Porous media equations, Stochastic models",
author = "Ahmed, {N. U.} and S. Kerbal",
year = "2009",
month = "4",
language = "English",
volume = "13",
pages = "271--286",
journal = "Communications in Applied Analysis",
issn = "1083-2564",
publisher = "Dynamic Publishers",
number = "2",

}

TY - JOUR

T1 - Stochastic dynamic model for porous media equation describing underground resources

AU - Ahmed, N. U.

AU - Kerbal, S.

PY - 2009/4

Y1 - 2009/4

N2 - We consider a stochastic model for porous media flow. This is a degenerate nonlinear stochastic parabolic partial differential equation which may change type from parabolic to elliptic and vice versa. We present existence and regularity of weak solutions. We formulate certain control problems for aquifers (under ground water reservoirs) and discuss some open problems.

AB - We consider a stochastic model for porous media flow. This is a degenerate nonlinear stochastic parabolic partial differential equation which may change type from parabolic to elliptic and vice versa. We present existence and regularity of weak solutions. We formulate certain control problems for aquifers (under ground water reservoirs) and discuss some open problems.

KW - Aquifers

KW - Nonlinear stochastic partial differential equations

KW - Optimal feedback control laws

KW - Porous media equations

KW - Stochastic models

UR - http://www.scopus.com/inward/record.url?scp=69549086666&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=69549086666&partnerID=8YFLogxK

M3 - Article

VL - 13

SP - 271

EP - 286

JO - Communications in Applied Analysis

JF - Communications in Applied Analysis

SN - 1083-2564

IS - 2

ER -