On the Schrödinger equations with isotropic and anisotropic fourth-order dispersion
| dc.contributor.author | Villamizar-Roa, Elder J. | |
| dc.contributor.author | Banquet, Carlos | |
| dc.date.accessioned | 2023-05-26T13:45:45Z | |
| dc.date.available | 2023-05-26T13:45:45Z | |
| dc.date.issued | 2016-01-07 | |
| dc.description.abstract | This article concerns the Cauchy problem associated with the nonlinear fourth-order Schrodinger equation with isotropic and anisotropic mixed dispersion. This model is given by the equation i∂tu + ε∆u + δAu + λ|u|αu = 0, x ∈ ℝn, t ∈ℝ, where A is either the operator ∆2 (isotropic dispersion) or ∑di=1 ∂xixixixi, 1 ≤ d < n (anisotropic dispersion), and α, ε, λ are real parameters. We obtain local and global well-posedness results in spaces of initial data with low regularity, based on weak- Lp spaces. Our analysis also includes the biharmonic and anisotropic biharmonic equation (ε = 0); in this case, we obtain the existence of self-similar solutions because of their scaling invariance property. In a second part, we analyze the convergence of solutions for the nonlinear fourth-order Schrödinger equation. i∂tu + ε∆u + δ∆2u + λ|u|αu = 0, x ∈ ℝn, t ∈ ℝ, as ε approaches zero, in the H2-norm, to the solutions of the corresponding biharmonic equation i∂tu + δ∆2u + λ|u|αu = 0. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 20 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Villamizar-Roa, E. J., & Banquet, C. (2016). On the Schrödinger equations with isotropic and anisotropic fourth-order dispersion. <i>Electronic Journal of Differential Equations, 2016</i>(13), pp. 1-20. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/16885 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2016, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Fourth-order Schrödinger equation | |
| dc.subject | Biharmonic equation | |
| dc.subject | Local and global solutions | |
| dc.title | On the Schrödinger equations with isotropic and anisotropic fourth-order dispersion | |
| dc.type | Article |