On a Nonlinear Initial—Boundary Value Problem with Venttsel Type Boundary Conditions Arizing in Homogenization of Complex Heat Transfer Problems

Andrey Amosov and Nikita Krymov
Additional contact information
Andrey Amosov: Department of Mathematical and Computer Modelling, National Research University “Moscow Power Engineering Institute”, Krasnokazarmennay St. 14, 111250 Moscow, Russia
Nikita Krymov: Department of Mathematical and Computer Modelling, National Research University “Moscow Power Engineering Institute”, Krasnokazarmennay St. 14, 111250 Moscow, Russia

Mathematics, 2022, vol. 10, issue 11, 1-23

Abstract: We consider a non-standard nonlinear singularly perturbed 2D initial-boundary value problem with Venttsel type boundary conditions, arising in homogenization of radiative-conductive heat transfer problems. We establish existence, uniqueness and regularity of a weak solution v . We obtained estimates for the derivatives D t v , D 1 2 v , D 2 2 v , D 1 D 2 v with a qualified order in the small parameter ε .

Keywords: radiative—conductive heat transfer problem; nonlinear initial—boundary value problem; Venttsel type boundary conditions; regularity of weak solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/11/1890/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/11/1890/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:11:p:1890-:d:829057

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().