A two‐dimensional diffusion coefficient determination problem for the time‐fractional equation

2021 ◽  
Author(s):  
Durdimurod K. Durdiev ◽  
Askar A. Rahmonov ◽  
Zavqiddin R. Bozorov
Keyword(s):  
Diffusion Coefficient ◽  
Two Dimensional ◽  
Dimensional Diffusion ◽  
Fractional Equation

scholarly journals Effect of Suction Cycles and Suction Gradients on the Water Retention Properties of a Hard Clay

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Liufeng Chen ◽  
Hua Peng
Keyword(s):  
Diffusion Coefficient ◽  
Relative Humidity ◽  
Water Retention ◽  
Moisture Diffusion ◽  
Two Dimensional ◽  
Moisture Diffusion Coefficient ◽  
Dimensional Diffusion ◽  
Water Retention Properties ◽  
Cylindrical Samples ◽  
Hydration And Dehydration

The effect of suction cycles and suction gradients on a hard clay is investigated. The cylindrical samples of the hard clay are prepared to carry out the hydration and dehydration tests with different suction gradient and suction cycles. The results show that the suction gradient has little effect on the suction-water content relation, while the suction cycle has great effect on it, particularly the first cycle of hydration and dehydration. The apparent moisture diffusion coefficient of the hard clay has been identified by the use of a two-dimensional diffusion model. The moisture diffusion coefficient varies between 4.10−11 m2/s and 2.10−10 m2/s and it decreases during dehydration while the relative humidity is less than 85%. The results also show that the suction cycles play little effect on the moisture diffusion coefficient.

scholarly journals A 2D diffusion coefficient determination problem for the time-fractional equation

2020 ◽  
Author(s):  
Askar Rahmonov ◽  
D. K. Durdiev ◽  
Zavqiddin Bozorov
Keyword(s):  
Inverse Problem ◽  
Integral Equation ◽  
Diffusion Coefficient ◽  
Local Existence ◽  
Stability Estimate ◽  
Fractional Diffusion ◽  
Two Dimensional ◽  
Uniqueness Results ◽  
The Stability ◽  
Fractional Equation

In this paper, we consider two dimensional inverse problem for a fractional diffusion equation. The inverse problem is reduced to the equivalent integral equation. For solving this equation the contracted mapping principle is applied. The local existence and global uniqueness results are proven. Also the stability estimate is obtained.

Asymptotic analysis of some two-dimensional diffusion problems

1995 ◽  
Vol 448 (1933) ◽  
pp. 213-236 ◽  
Keyword(s):  
Linear Problem ◽  
Vacancy Concentration ◽  
Surface Concentration ◽  
Two Dimensional ◽  
Surface Source ◽  
Dimensional Diffusion ◽  
Equilibrium Vacancy ◽  
Equilibrium Vacancy Concentration ◽  
Dimensional Surface ◽  
Diffusion Problems

In this paper we discuss two-dimensional surface source and implant problems for a substitutional-interstitial diffusion model. We present asymptotic solutions in the limit of the surface concentration of impurity (or peak concentration of the implant) being far greater than the equilibrium vacancy concentration. Using leading order composite solutions we plot contours of constant impurity concentration. Some of these contours differ markedly from those of the corresponding linear problem, having the ‘bird’s beak’ shape which is frequently observed in experiments. We also discuss a two-dimensional surface source problem for a va­cancy model.

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