Nonlocal abstract Ginzburg–Landau-type equations and applications

Shakhmurov V.

Theoretical and Mathematical Physics (Russian Federation), vol.221, no.2, pp.1867-1881, 2024 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 221 Issue: 2
  • Publication Date: 2024
  • Doi Number: 10.1134/s0040577924110060
  • Journal Name: Theoretical and Mathematical Physics (Russian Federation)
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1867-1881
  • Keywords: -regularity property of solutions, diffusion equations, dissipative operators, embedding in Sobolev and Besov spaces, Fourier multipliers, Ginzburg–Landau equation
  • Open Archive Collection: Article
  • Azerbaijan State University of Economics (UNEC) Affiliated: No

Abstract

Abstract: We study a nonlocal abstract Ginzburg–Landau type equation. The equation includes variable coefficients with convolution terms and an abstract linear operator function in a Fourier-type Banach space. For sufficiently smooth initial data, assuming growth conditions for the operator and the coefficient, the existence and uniqueness of the solution and the -regularity properties are established. We obtain the existence and uniqueness of the solution, and the regularity of different classes of nonlocal Ginzburg–Landau-type equations by choosing the space and operator that occur in a wide variety of physical systems.