On the principle of limiting amplitude
Nobuhisa Iwasaki · Publications of the Research Institute for Mathematical Sciences · 1967
and the Sommerfeld radiation conditions at infinity. A denotes the Laplacian in E and o* is a real number. In the case when &(#)=0 and the real valued function £(#) is once continuously differentiable and its support is compact, this principle has been proved by O. A. Ladyzenskaja [1] . Here the rate of approach to steady state is like e~, e>0 as £-^oo. When b(x) and c(#) satisfy that i(jc)=0(-1—wr), c(jc)=0(-|—r^J as |^|->oo, and others, S. Mizohata i x I / I x I / and K. Mochizuki [2] had shown the principle, but they did not give the rate of approach. In this paper we shall obtain the rate e~ under the assumption that the real valued functions K#)>0, £(#)I>0 are bounded and their supports are compact.