Email this article $L_p$-approximations for solutions of parabolic differential equations on manifolds
- Authors: Smirnova A.S.1
-
Affiliations:
- Higher School of Economics
- Issue: Vol 24, No 3 (2022)
- Pages: 297-303
- Section: Mathematics
- Published: 24.08.2022
- URL: https://ogarev-online.ru/2079-6900/article/view/366177
- DOI: https://doi.org/10.15507/2079-6900.24.202203.297-303
- ID: 366177
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Abstract
The paper considers the Cauchy problem for a parabolic partial differential equation in a Riemannian manifold of bounded geometry. A formula is given that expresses arbitrarily accurate (in the $L_p$-norm) approximations to the solution of the Cauchy problem in terms of parameters - the coefficients of the equation and the initial condition. The manifold is not assumed to be compact, which creates significant technical difficulties - for example, integrals over the manifold become improper in the case when the manifold has an infinite volume. The presented approximation method is based on Chernoff theorem on approximation of operator semigroups.
About the authors
Anna S. Smirnova
Higher School of Economics
Author for correspondence.
Email: smirnovaas@hse.ru
ORCID iD: 0000-0003-4172-2811
Postgraduate Student, Department of Fundamental Mathematics
Russian Federation, 25/12 B. Pecherskaya St., Nizhny Novgorod 603150, RussiaReferences
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