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Solving the Fractional Schrödinger Equation with Singular Initial Data in the Extended Colombeau Algebra of Generalized Functions.
- Source :
-
International Journal of Differential Equations . 5/2/2023, p1-10. 10p. - Publication Year :
- 2023
-
Abstract
- This manuscript aims to highlight the existence and uniqueness results for the following Schrödinger problem in the extended Colombeau algebra of generalized functions. 1 / ı ∂ / ∂ t u t , x − △ u t , x + v x u t , x = 0 , t ∈ R + , x ∈ R n , v x = δ x , u 0 , x = δ x , where δ is the Dirac distribution. The proofs of our main results are based on the Gronwall inequality and regularization method. We conclude our article by establishing the association concept of solutions. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 16879643
- Database :
- Academic Search Index
- Journal :
- International Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 163484193
- Full Text :
- https://doi.org/10.1155/2023/3493912