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EnglishWe study the large-time behavior of solutions to the nonlinear exterior problem Lu(t, x) = κ[pipe]u(t, x)[pipe]p, (t, x) ∈ (0, ∞) x Dc under the nonhomegeneous Neumann boundary condition (t, x) = λ(x), (t, x) ∈ (0, ∞) x ∂D, where L:= i∂t + Δ is the Schrodinger operator, D = B(0, 1) is the open unit ball in RN, N ≥ 2, Dc = RND, p > 1, κ ∈ , κ ≠ 0, λ ∈ L1(∂D, ) is a nontrivial complex valued function, and ∂v is the outward unit normal vector on ∂D, relative to Dc. Namely, under a certain condition imposed on (κ, λ), we show that if N ≥ 3 and p < pc, where pc =, then the considered problem admits no global weak solutions. However, if N = 2, then for all p > 1, the problem admits no global weak solutions. The proof is based on the test function method introduced by Mitidieri and Pohozaev, and an adequate choice of the test function.
Alqahtani A., Jleli M., Samet B., & Vetro C. (2020). Nonexistence of global weak solutions for a nonlinear Schrodinger equation in an exterior domain. SYMMETRY, 12(3), 1-9 [10.3390/sym12030394].
| Data di pubblicazione: | 2020 | |
| Titolo: | Nonexistence of global weak solutions for a nonlinear Schrodinger equation in an exterior domain | |
| Autori: | ||
| Citazione: | Alqahtani A., Jleli M., Samet B., & Vetro C. (2020). Nonexistence of global weak solutions for a nonlinear Schrodinger equation in an exterior domain. SYMMETRY, 12(3), 1-9 [10.3390/sym12030394]. | |
| Rivista: | ||
| Digital Object Identifier (DOI): | http://dx.doi.org/10.3390/sym12030394 | |
| Abstract: | We study the large-time behavior of solutions to the nonlinear exterior problem Lu(t, x) = κ[pipe]u(t, x)[pipe]p, (t, x) ∈ (0, ∞) x Dc under the nonhomegeneous Neumann boundary condition (t, x) = λ(x), (t, x) ∈ (0, ∞) x ∂D, where L:= i∂t + Δ is the Schrodinger operator, D = B(0, 1) is the open unit ball in RN, N ≥ 2, Dc = RND, p > 1, κ ∈ , κ ≠ 0, λ ∈ L1(∂D, ) is a nontrivial complex valued function, and ∂v is the outward unit normal vector on ∂D, relative to Dc. Namely, under a certain condition imposed on (κ, λ), we show that if N ≥ 3 and p < pc, where pc =, then the considered problem admits no global weak solutions. However, if N = 2, then for all p > 1, the problem admits no global weak solutions. The proof is based on the test function method introduced by Mitidieri and Pohozaev, and an adequate choice of the test function. | |
| Settore Scientifico Disciplinare: | Settore MAT/05 - Analisi Matematica | |
| Appare nelle tipologie: | 1.01 Articolo in rivista |
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| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| symmetry-12-00394.pdf | Articolo principale | Versione Editoriale | Open Access Visualizza/Apri |
http://hdl.handle.net/10447/412554
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