Separability Properties of Differential Operators in Exterior Regions and Applications

Shakhmurov V. B.

LOBACHEVSKII JOURNAL OF MATHEMATICS, vol.44, no.12, pp.5406-5418, 2023 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 12
  • Publication Date: 2023
  • Doi Number: 10.1134/s1995080223120302
  • Journal Name: LOBACHEVSKII JOURNAL OF MATHEMATICS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Page Numbers: pp.5406-5418
  • Azerbaijan State University of Economics (UNEC) Affiliated: No

Abstract

The abstract elliptic and parabolic equations on exterior regions are considered. The equations have top-order variable coefficients. The separability properties of boundary value problems for elliptic equation and well-posedness of the Cauchy problem for parabolic equations are established. We obtain the maximal regularity properties of a wide class of elliptic and parabolic equations by choosing the space E and the operator A which appear in the field of physics. In application, the maximal regularity properties of Cauchy problem for anisotropic parabolic equations and system of parabolic equations are derived