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<p>We study a parabolic initial boundary-value problem for a system of two differential equations with two different types (Dirichlet and Neumann) of boundary conditions. This happens, in particular, in the theory of heat-and-mass transfer. We establish sufficient conditions for the generalized solution of the problem to be classical formulated in terms of belonging of the problem data to generalized anisotropic Sobolev spaces.</p>

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ON THE CLASSICAL NATURE OF SOLUTIONS OF THE BOUNDARY-VALUE PROBLEM FOR A SECOND-ORDER PARABOLIC SYSTEM

  • 期刊论文

  • 发表日期：

    2025年7月30日

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  • Oleksandr Diachenko,
  • Valerii Los

摘要

We study a parabolic initial boundary-value problem for a system of two differential equations with two different types (Dirichlet and Neumann) of boundary conditions. This happens, in particular, in the theory of heat-and-mass transfer. We establish sufficient conditions for the generalized solution of the problem to be classical formulated in terms of belonging of the problem data to generalized anisotropic Sobolev spaces.