Local Time Decay for a Quasilinear Schrodinger Equation

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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Published 1 January 2009