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

Author

Listed:
  • 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)

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 .

Suggested Citation

  • Andrey Amosov & Nikita Krymov, 2022. "On a Nonlinear Initial—Boundary Value Problem with Venttsel Type Boundary Conditions Arizing in Homogenization of Complex Heat Transfer Problems," Mathematics, MDPI, vol. 10(11), pages 1-23, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1890-:d:829057
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