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🔗 Source: jnas.nbuv.gov.ua
📊 Size: 470 KB
📄 Pages: 16 pages
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The article discusses sufficient conditions for the classical solvability of mixed parabolic problems. The problem is considered in a cylinder with a smooth boundary, and the equation is a second-order linear parabolic equation with a Dirichlet boundary condition. The authors obtain new sufficient conditions for the classical solvability of the problem, which are formulated in terms of the belonging of the right-hand sides of the problem to certain 2b-anisotropic Hörmander spaces. The classical solutions can be discontinuous on the junction of the lateral area and base of the cylinder. The results are applied to a mixed problem for a linear parabolic differential equation of the second order with a Dirichlet boundary condition. The sufficient conditions are formulated in terms of the belonging of the right-hand sides of the problem to the corresponding Hörmander spaces, which allows for more subtle sufficient conditions than those possible within the framework of classical scales of functional spaces of Hölder and Sobolev.

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The article discusses sufficient conditions for the classical solvability of mixed parabolic problems.

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  • File Format: PDF
  • File Size: 470 KB
  • Pages: 16
  • Language: EN
  • Total Downloads: 83
  • Last Updated: 3 weeks ago

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