Boundary-Value Problem for the Aller–Lykov Nonlocal Moisture Transfer Equation
In this paper, a boundary-value problem for the inhomogeneous Aller–Lykov moisture transfer equation with a fractional Riemann–Liouville time derivative is examined. The equation considered is a generalization of the Aller–Lykov equation obtained by introducing the fractal rate of change of humidity...
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| Published in | Journal of mathematical sciences (New York, N.Y.) Vol. 260; no. 3; pp. 300 - 306 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.01.2022
Springer Springer Nature B.V |
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| Online Access | Get full text |
| ISSN | 1072-3374 1573-8795 |
| DOI | 10.1007/s10958-022-05694-2 |
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| Abstract | In this paper, a boundary-value problem for the inhomogeneous Aller–Lykov moisture transfer equation with a fractional Riemann–Liouville time derivative is examined. The equation considered is a generalization of the Aller–Lykov equation obtained by introducing the fractal rate of change of humidity, which explains the appearance of flows directed against the potential of humidity. The existence of a solution to the first boundary-value problem is proved by the Fourier method. Using the method of energy inequalities for solutions of the problem, we obtain an a priori estimate in terms of the fractional Riemann–Liouville derivative, which implies the uniqueness of the solution. |
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| AbstractList | In this paper, a boundary-value problem for the inhomogeneous Aller--Lykov moisture transfer equation with a fractional Riemann--Liouville time derivative is examined. The equation considered is a generalization of the Aller--Lykov equation obtained by introducing the fractal rate of change of humidity, which explains the appearance of flows directed against the potential of humidity. The existence of a solution to the first boundary-value problem is proved by the Fourier method. Using the method of energy inequalities for solutions of the problem, we obtain an a priori estimate in terms of the fractional Riemann--Liouville derivative, which implies the uniqueness of the solution. In this paper, a boundary-value problem for the inhomogeneous Aller--Lykov moisture transfer equation with a fractional Riemann--Liouville time derivative is examined. The equation considered is a generalization of the Aller--Lykov equation obtained by introducing the fractal rate of change of humidity, which explains the appearance of flows directed against the potential of humidity. The existence of a solution to the first boundary-value problem is proved by the Fourier method. Using the method of energy inequalities for solutions of the problem, we obtain an a priori estimate in terms of the fractional Riemann--Liouville derivative, which implies the uniqueness of the solution. Keywords and phrases: Aller--Lykov moisture transfer equation, Riemann--Liouville fractional derivative, Fourier method, a priori estimate, method of energy inequalities. AMS Subject Classification: 35L99 |
| Audience | Academic |
| Author | Gekkieva, S. Kh Kerefov, M. A. |
| Author_xml | – sequence: 1 givenname: S. Kh surname: Gekkieva fullname: Gekkieva, S. Kh email: gekkieva_s@mail.ru organization: Institute of Applied Mathematics and Automation of the Kabardino-Balkar Scientific Center of the Russian Academy of Sciences – sequence: 2 givenname: M. A. surname: Kerefov fullname: Kerefov, M. A. organization: Kabardino-Balkarian State University named after H. M. Berbekov |
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| Keywords | Aller–Lykov moisture transfer equation method of energy inequalities Riemann–Liouville fractional derivative 35L99 Fourier method a priori estimate |
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| References | CR2 CR3 CR6 CR5 CR8 CR7 Lafisheva, Kerefov, Dyshekova (CR9) 2017; 19 CR17 CR16 CR15 CR14 Agrawal (CR1) 2002; 29 CR13 CR12 CR11 CR10 Gekkieva (CR4) 1994; 1 OP Agrawal (5694_CR1) 2002; 29 5694_CR13 5694_CR14 MM Lafisheva (5694_CR9) 2017; 19 5694_CR15 SK Gekkieva (5694_CR4) 1994; 1 5694_CR16 5694_CR10 5694_CR11 5694_CR12 5694_CR6 5694_CR7 5694_CR8 5694_CR2 5694_CR17 5694_CR3 5694_CR5 |
| References_xml | – volume: 19 start-page: 50 issue: 1 year: 2017 end-page: 58 ident: CR9 article-title: Finite-difference schemes for the Aller–Lykov moisture transfer equation with a nonlocal condition publication-title: Vladikavkaz Mat. Zh. – ident: CR3 – ident: CR14 – ident: CR15 – ident: CR2 – ident: CR16 – volume: 1 start-page: 16 issue: 1 year: 1994 end-page: 19 ident: CR4 article-title: Boundary-value problem for a generalized transfer equation with a fractional derivative by time publication-title: Dokl. Adyg. (Cherkes.) Mezhdunar. Akad. Nauk. – ident: CR12 – ident: CR17 – ident: CR13 – ident: CR10 – ident: CR11 – ident: CR6 – ident: CR5 – ident: CR7 – ident: CR8 – volume: 29 start-page: 145 year: 2002 end-page: 155 ident: CR1 article-title: Solution for a fractional diffusion-wave equation defined in a bounded domain publication-title: Nonlin. Dynam. doi: 10.1023/A:1016539022492 – ident: 5694_CR17 – volume: 29 start-page: 145 year: 2002 ident: 5694_CR1 publication-title: Nonlin. Dynam. doi: 10.1023/A:1016539022492 – ident: 5694_CR16 – ident: 5694_CR15 – ident: 5694_CR11 – ident: 5694_CR12 – ident: 5694_CR13 – volume: 19 start-page: 50 issue: 1 year: 2017 ident: 5694_CR9 publication-title: Vladikavkaz Mat. Zh. – ident: 5694_CR14 – ident: 5694_CR7 – ident: 5694_CR6 – ident: 5694_CR5 – ident: 5694_CR10 – ident: 5694_CR2 – ident: 5694_CR3 – volume: 1 start-page: 16 issue: 1 year: 1994 ident: 5694_CR4 publication-title: Dokl. Adyg. (Cherkes.) Mezhdunar. Akad. Nauk. – ident: 5694_CR8 |
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| Snippet | In this paper, a boundary-value problem for the inhomogeneous Aller–Lykov moisture transfer equation with a fractional Riemann–Liouville time derivative is... In this paper, a boundary-value problem for the inhomogeneous Aller--Lykov moisture transfer equation with a fractional Riemann--Liouville time derivative is... |
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| SubjectTerms | Boundary value problems Humidity Mathematical analysis Mathematics Mathematics and Statistics Moisture |
| Title | Boundary-Value Problem for the Aller–Lykov Nonlocal Moisture Transfer Equation |
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