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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
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