NDLI: On a Fractional in Time Nonlinear Schrödinger Equation with Dispersion Parameter and Absorption Coefficient

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On a Fractional in Time Nonlinear Schrödinger Equation with Dispersion Parameter and Absorption Coefficient

Content Provider	MDPI
Author	Jleli, Mohamed Samet, Bessem Vetro, Calogero
Copyright Year	2020
Abstract	This paper is concerned with the nonexistence of global solutions to fractional in time nonlinear Schrödinger equations of the form $i^{α} \partial_{t}^{α} ω (t, z) + a_{1} (t) Δ ω (t, z) + i^{α} a_{2} (t) ω (t, z) = ξ {\| ω (t, z) \|}^{p}, (t, z) \in (0, \infty) \times R^{N}$ , where $N \geq 1$ , $ξ \in C \ {0}$ and $p > 1$ , under suitable initial data. To establish our nonexistence theorem, we adopt the Pohozaev nonlinear capacity method, and consider the combined effects of absorption and dispersion terms. Further, we discuss in details some special cases of coefficient functions $a_{1}, a_{2} \in L_{l o c}^{1} ([0, \infty), R)$ , and provide two illustrative examples.
Starting Page	1197
e-ISSN	20738994
DOI	10.3390/sym12071197
Journal	Symmetry
Issue Number	7
Volume Number	12
Language	English
Publisher	MDPI
Publisher Date	2020-07-20
Access Restriction	Open
Subject Keyword	Symmetry Mathematical Physics Fractional in Time Nonlinear Schrödinger Equation Absorption Coefficient Dispersion Parameter Global Solution
Content Type	Text
Resource Type	Article

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