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Volume 24, Issue 1
Decay of Solutions to a 2D Schrodinger Equation

Tarek Saanouni

DOI: 10.4208/jpde.v24.n1.3

J. Part. Diff. Eq., 24 (2011), pp. 37-54.

Published online: 2011-02

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  • Abstract

Let u∈C(R,H^1) be the solution to the initial value problem for a 2D semilinear Schrödinger equation with exponential type nonlinearity, given in [1]. We prove that the L^r norms of u decay as t→±∞, provided that r > 2.

  • Keywords

Nonlinear Schrödinger equation well-posedness scattering theory Trudinger-Moser inequality

  • AMS Subject Headings

35L70 35Q55 35B40 35B33 37K05 37L50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-24-37, author = {Tarek Saanouni }, title = {Decay of Solutions to a 2D Schrodinger Equation}, journal = {Journal of Partial Differential Equations}, year = {2011}, volume = {24}, number = {1}, pages = {37--54}, abstract = {

Let u∈C(R,H^1) be the solution to the initial value problem for a 2D semilinear Schrödinger equation with exponential type nonlinearity, given in [1]. We prove that the L^r norms of u decay as t→±∞, provided that r > 2.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v24.n1.3}, url = {http://global-sci.org/intro/article_detail/jpde/5196.html} }
TY - JOUR T1 - Decay of Solutions to a 2D Schrodinger Equation AU - Tarek Saanouni JO - Journal of Partial Differential Equations VL - 1 SP - 37 EP - 54 PY - 2011 DA - 2011/02 SN - 24 DO - http://doi.org/10.4208/jpde.v24.n1.3 UR - https://global-sci.org/intro/article_detail/jpde/5196.html KW - Nonlinear Schrödinger equation KW - well-posedness KW - scattering theory KW - Trudinger-Moser inequality AB -

Let u∈C(R,H^1) be the solution to the initial value problem for a 2D semilinear Schrödinger equation with exponential type nonlinearity, given in [1]. We prove that the L^r norms of u decay as t→±∞, provided that r > 2.

Tarek Saanouni . (2011). Decay of Solutions to a 2D Schrodinger Equation. Journal of Partial Differential Equations. 24 (1). 37-54. doi:10.4208/jpde.v24.n1.3
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