TY - JOUR

T1 - On an inverse problem of reconstructing a subdiffusion process from nonlocal data

AU - Kirane, Mokhtar

AU - Sadybekov, Makhmud A.

AU - Sarsenbi, Abdisalam A.

N1 - Funding Information:
The first named author is supported by NAAM group, King Abdulaziz university, Jeddah. The second and third named authors were supported in parts by the MES RK grant AP05133271 and by the MES RK target program BR05236656.
Publisher Copyright:
© 2019 John Wiley & Sons, Ltd.

PY - 2019/4

Y1 - 2019/4

N2 - We consider a problem of modeling the thermal diffusion process in a closed metal wire wrapped around a thin sheet of insulation material. The layer of insulation is assumed to be slightly permeable. Therefore, the temperature value from one side affects the diffusion process on the other side. For this reason, the standard heat equation is modified, and a third term with an involution is added. Modeling of this process leads to the consideration of an inverse problem for a one-dimensional fractional evolution equation with involution and with periodic boundary conditions with respect to a space variable. This equation interpolates heat equation. Such equations are also called nonlocal subdiffusion equations or nonlocal heat equations. The inverse problem consists in the restoration (simultaneously with the solution) of the unknown right-hand side of the equation, which depends only on the spatial variable. The conditions for overdefinition are initial and final states. Existence and uniqueness results for the given problem are obtained via the method of separation of variables.

AB - We consider a problem of modeling the thermal diffusion process in a closed metal wire wrapped around a thin sheet of insulation material. The layer of insulation is assumed to be slightly permeable. Therefore, the temperature value from one side affects the diffusion process on the other side. For this reason, the standard heat equation is modified, and a third term with an involution is added. Modeling of this process leads to the consideration of an inverse problem for a one-dimensional fractional evolution equation with involution and with periodic boundary conditions with respect to a space variable. This equation interpolates heat equation. Such equations are also called nonlocal subdiffusion equations or nonlocal heat equations. The inverse problem consists in the restoration (simultaneously with the solution) of the unknown right-hand side of the equation, which depends only on the spatial variable. The conditions for overdefinition are initial and final states. Existence and uniqueness results for the given problem are obtained via the method of separation of variables.

KW - equation with involution

KW - fractional evolution equation

KW - inverse problem

KW - method of separation of variables

KW - nonlocal heat equation

KW - nonlocal subdiffusion equation

KW - periodic boundary conditions

UR - http://www.scopus.com/inward/record.url?scp=85061255943&partnerID=8YFLogxK

U2 - 10.1002/mma.5498

DO - 10.1002/mma.5498

M3 - Article

AN - SCOPUS:85061255943

SN - 0170-4214

VL - 42

SP - 2043

EP - 2052

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 6

ER -