## On stabilization of the Poisson integral and Tikhonov-Stieltjes means: two-sided estimate.(English. Russian original)Zbl 1477.35005

Dokl. Math. 103, No. 1, 32-34 (2021); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 496, 40-43 (2021).
Summary: We establish two-sided estimates for the proximity, as $$t \to \infty$$, of the Poisson integral representing the solution of the Cauchy problem for the heat equation to modified Tikhonov-Stieltjes means of the initial function. Order-sharp two-sided estimates in some classes of initial functions are described.

### MSC:

 35A23 Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals 35K15 Initial value problems for second-order parabolic equations

### Keywords:

stabilization; heat equation; Cauchy problem
Full Text:

### References:

 [1] Tikhonov, A. N., Mat. Sb., 45, 198-216 (1935) [2] Tikhonov, A. N., Dokl. Akad. Nauk SSSR, 156, 268-271 (1964) [3] Denisov, V. N., Differ. Uravn., 21, 30-40 (1985) [4] Denisov, V. N., Russ. Math. Surv., 60, 721-790 (2005) · Zbl 1149.35300 [5] Denisov, V. N., Sovrem. Mat. Fundam. Napravlen., 6, 1-155 (2020) [6] Denisov, V. N.; Repnikov, V. D., Differ. Uravn., 20, 20-41 (1984) [7] Denisov, V. N.; Zhikov, V. V., Math. Notes, 37, 456-466 (1985) · Zbl 0593.35015
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.