Dafermos regularization of a diffusive-dispersive equation with cubic flux

Monique Taylor; Stephen Schecter

doi:10.3934/dcds.2012.32.4069

Dafermos regularization of a diffusive-dispersive equation with cubic flux

Discrete and Continuous Dynamical Systems ◽

10.3934/dcds.2012.32.4069 ◽

2012 ◽

Vol 32 (12) ◽

pp. 4069-4110 ◽

Cited By ~ 1

Author(s):

Monique Taylor ◽

Stephen Schecter

Keyword(s):

Dispersive Equation ◽

Dafermos Regularization

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Optimal control of a viscous generalized θ-type dispersive equation with weak dissipation

Open Mathematics ◽

10.1515/math-2020-0075 ◽

2020 ◽

Vol 18 (1) ◽

pp. 1302-1316

Author(s):

Guobing Fan ◽

Zhifeng Yang

Keyword(s):

Boundary Condition ◽

Optimal Control ◽

Weak Solution ◽

Existence And Uniqueness ◽

Optimal Solution ◽

Dispersive Equation ◽

Weak Dissipation ◽

Formula Type

Abstract In this paper, we investigate the problem for optimal control of a viscous generalized \theta -type dispersive equation (VG \theta -type DE) with weak dissipation. First, we prove the existence and uniqueness of weak solution to the equation. Then, we present the optimal control of a VG \theta -type DE with weak dissipation under boundary condition and prove the existence of optimal solution to the problem.

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Channeling Flow and Solute Transport in a Single Fracture

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.316-317.632 ◽

2013 ◽

Vol 316-317 ◽

pp. 632-635

Author(s):

Ye Fei Tan ◽

Zhi Fang Zhou ◽

Shi Qiang Wu ◽

Xing Hua Xie ◽

Bo Ning

Keyword(s):

Finite Element Method ◽

Drinking Water ◽

Breakthrough Curve ◽

Laboratory Experiments ◽

Fractured Media ◽

Single Fracture ◽

The Finite Element Method ◽

Dispersive Equation ◽

One Dimensional ◽

Channeling Flow

Groundwater in fractured media plays an important role in drinking water supply, and the understanding of its principle mechanisms is essential for securing the groundwater exploring and utilization. In this paper, a novel conceptual fracture model was presented on the basis of the reality of channeling flow in natural fractures and laboratory experiments were conducted for the purpose of getting a better understanding of the step-like breakthrough curve (BTC). Experimental results were fitted with convective dispersive equation (CDE) and compared with those of the finite element method (FEM) models. Results showed that the traditional one-dimensional CDE was invalid in the fitting of a step-like BTC and needed to be improved.

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