Boundary-Value Problem for the Aller–Lykov Nonlocal Moisture Transfer Equation

• Published in: Journal of mathematical sciences (New York, N.Y.) Vol. 260; no. 3; pp. 300 - 306
• Main Authors: Gekkieva, S. Kh, Kerefov, M. A.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.01.2022; Springer; Springer Nature B.V
• Subjects: Boundary value problems; Humidity; Mathematical analysis; Mathematics; Mathematics and Statistics; Moisture; Aller–Lykov moisture transfer equation; method of energy inequalities; Riemann–Liouville fractional derivative; 35L99; Fourier method; a priori estimate
• ISSN: 1072-3374; 1573-8795
• DOI: 10.1007/s10958-022-05694-2

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.