Solvability of Some Integro-Differential Equations with Transport and Concentrated Sources

Efendiev M., Vougalter V.

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, vol.36, no.3, pp.1967-1980, 2024 (SCI-Expanded, Scopus) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 3
  • Publication Date: 2024
  • Doi Number: 10.1007/s10884-022-10212-8
  • Journal Name: JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.1967-1980
  • Keywords: Integro-differential equations, Dirac delta function, Non-Fredholm operators, Sobolev spaces, NONLINEAR SCHRODINGER-EQUATION, PROPERNESS PROPERTIES, ELLIPTIC-OPERATORS, HOLDER THEORY, FREDHOLM, DIFFUSION, DIRICHLET, EXISTENCE, SYSTEMS
  • Marmara University Affiliated: No

Abstract

The work deals with the existence of solutions of an integro-differential equation in the case of the normal diffusion and the influx/efflux term proportional to the Dirac delta function in the presence of the drift term. The proof of the existence of solutions relies on a fixed point technique. We use the solvability conditions for the non-Fredholm elliptic operators in unbounded domains and discuss how the introduction of the transport term influences the regularity of the solutions.