# 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 language English 271-286 16 Communications in Applied Analysis 13 2 Published - 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

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

Research output: Contribution to journalArticle

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