Methods and Applications of Analysis

Volume 16 (2009)

Number 3

Local Time Decay for a Quasilinear Schrodinger Equation

Pages: 313 – 320

DOI: http://dx.doi.org/10.4310/MAA.2009.v16.n3.a3

Author

J. E. Lin

Abstract

We study the solutions of a quasilinear Schrödinger equation which has been derived in many areas of physical modeling. Using the Morawetz Radial Identity, we show that the local energy of a solution is integrable in time and the local $L^2$ norm of the solution approaches zero as time approaches the infinity.

Keywords

Time decay; quasilinear Schrödinger equation

2010 Mathematics Subject Classification

35Q55

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