Well-posedness of nonlocal Ginzburg–Landau type equations

Shakhmurov V., Shahmurov R.

European Journal of Mathematics, vol.10, no.4, 2024 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 4
  • Publication Date: 2024
  • Doi Number: 10.1007/s40879-024-00772-y
  • Journal Name: European Journal of Mathematics
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH
  • Keywords: 35B35, 35B40, 35B41, 35B65, 35J50, 35Q35, Diffusion equations, Embedding in Sobolev spaces, Fourier multipliers, Ginzburg–Landau equation, Lp-regularity property of solutions
  • Azerbaijan State University of Economics (UNEC) Affiliated: No

Abstract

The Cauchy problem for linear and nonlinear Ginzburg–Landau type equations is studied. The equation includes variable coefficients with convolution terms. Assuming enough smoothness of the initial data and certain growth conditions on coefficients, the existence, uniqueness of local and global solution, Lp-regularity, and blow-up properties of solutions are established.