ON THE ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF THE WAVE EQUATION OF HARTREE TYPE

Paschalis Karageorgis, Kimitoshi Tsutaya

Abstract


We study the scattering problem for the wave equation of Hartreetype with small initial data of slow decay. We show the existence of the scatteringoperator under some conditions. We also show that those conditions aresharp by presenting a non scattering result. In the present paper, we introducea modified weighted norm as a new tool.

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