Recovering Source Term and Temperature Distribution for Nonlocal Heat Equation

Ilyas, Asim; Malik, Salman A.; Saif, Summaya

doi:10.1016/j.amc.2022.127610

Cited by 3 publications

(4 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We have already obtained uniqueness of the source term q(t) by using Banach fixed point theorem. v(x, t) can be proved by considering v 1 (x, t) and v 2 (x, t) as the two regular solution set of the ISP-II (1)-( 5) and (7), and finding them equal, that is, v 1 (x, t) = v 2 (x, t) by using the fact that bi-orthogonal systems of functions ( 14) form a complete set in L 2 ((0, 1)). □…”

Section: Uniqueness Of the Solution Of The Isp-iimentioning

confidence: 99%

“…ISPs for a diffusion equations with nonlocal boundary conditions are studied, see [7,8]. The nonlocal boundary conditions arise in many physical phenomena, see, for example, [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

“…This motivates the exploration and investigation of nonlocal boundary‐value problems. ISPs for a diffusion equations with nonlocal boundary conditions are studied, see [7, 8]. The nonlocal boundary conditions arise in many physical phenomena, see, for example, [9–11].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Identifying temperature distribution and source term for generalized diffusion equation with arbitrary memory kernel

Ilyas,

Khalid,

Malik

2024

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

A diffusion equation involving integral convolution in time variable with arbitrary kernel and nonlocal boundary conditions is considered. The existence and uniqueness results for two inverse problems of determining source terms (space‐ and time‐dependent sources) along with diffusion concentration from appropriate over‐specified conditions are presented. A bi‐orthogonal system of functions is used to have series representation of the solutions of the inverse problems. Several special cases such as standard diffusion, multi‐term diffusion, and tempered diffusion equations are discussed, and some examples are provided.

show abstract

Section: Uniqueness Of the Solution Of The Isp-iimentioning

confidence: 99%

“…ISPs for a diffusion equations with nonlocal boundary conditions are studied, see [7,8]. The nonlocal boundary conditions arise in many physical phenomena, see, for example, [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Identifying temperature distribution and source term for generalized diffusion equation with arbitrary memory kernel

Ilyas,

Khalid,

Malik

2024

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

“…Several properties of the Dzherbashian-Nersesian FD have been proved in Ahmad et al [12]. In Asim et al [13,14], FOOs usually Know as nth level FD has been shown to be generalization of well-known functions such as HFD, CFD and RFD and ISPs for a time-fractional diffusion equations (TFDEs) with nth level FD are considered. DPs for diffusion equations involving non-classical BCs are studied in the works [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

On the solvability of direct and inverse problems for a generalized diffusion equation

Ilyas,

Malik,

Saif

2023

Phys. Scr.

Self Cite

View full text Add to dashboard Cite

This paper investigates direct and two inverse source problems for a diﬀusion equation involving integral convolution in time, subject to non-classical boundary conditions. The inverse source problems are proved to be ill-posed in the sense of Hadamard. A bi-orthogonal system of functions is used to write the series solutions of the inverse source problems. The unique existence of series solutions is obtained by imposing certain conditions on the given data. Some speciﬁc cases for the diﬀusion equation are given depending on the type of memory kernel. Furthermore, some particular examples are also formulated to illustrate the obtained results for the inverse source problems.

show abstract