A stability estimate on the regularized solution of the backward heat equation

Yıldız, Bünyamin; Yetişkin, Hakan; Sever, Ali

doi:10.1016/s0096-3003(02)00069-3

Cited by 17 publications

(3 citation statements)

References 2 publications

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“…In the case of constant or time-dependent diffusion coefficient, the classical backward heat conduction equation has been studied in many works, see for example, other studies. [8][9][10] However, to the best of our knowledge, there are not any result on (1)(2)(3). Our paper is the first study on this direction for parabolic systems with random model.…”

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confidence: 82%

“…Among them, the most successful model is used to describe population density in biology or particle density in material science. In order to study the interaction of two or more biological species, systems of parabolic equations have been proposed; see Hao et al 7 Problem (–) brought significant question that is “If we have the density of the two species at the present time, how to determine their density at a previous time?” In the case of constant or time‐dependent diffusion coefficient, the classical backward heat conduction equation has been studied in many works, see for example, other studies 8–10 . However, to the best of our knowledge, there are not any result on (–).…”

Section: Introductionmentioning

confidence: 99%

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Recovering the initial value for a system of nonlocal diffusion equations with random noise on the measurements

Triet

Binh²,

Phương

et al. 2020

Math Methods in App Sciences

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In this work, we study the final value problem for a system of parabolic diffusion equations. In which, the final value functions are derived from a random model. This problem is severely ill‐posed in the sense of Hadamard. By nonparametric estimation and truncation methods, we offer a new regularized solution. We also investigate an estimate of the error and a convergence rate between a mild solution and its regularized solutions. Finally, some numerical experiments are constructed to confirm the efficiency of the proposed method.

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confidence: 82%

Section: Introductionmentioning

confidence: 99%

Recovering the initial value for a system of nonlocal diffusion equations with random noise on the measurements

Triet

Binh²,

Phương

et al. 2020

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…A modified quasi-reversibility for problem (1.2) is investigeted by Denche et al [3], Fu et al [8]. Optimal filtering method for (1.2) is established by Seidman [11] Stability estimate on the homogeneous backward heat has been studied by Yildiz et al [16]. Very recently, problem (1.2) was also investigated by Wang [15].…”

Section: Introductionmentioning

confidence: 99%