Bl. Guo et Cx. Miao, GLOBAL EXISTENCE AND ASYMPTOTIC-BEHAVIOR OF SOLUTIONS FOR THE COUPLEDKLEIN-GORDON-SCHRODINGER EQUATIONS, Science in China. Series A, Mathematics, Physics, Astronomy & Technological Sciences, 38(12), 1995, pp. 1444-1456
The final value problem for the classical coupled Klein-Gordon-Schrodi
nger equations is, studied in R(1+n). This leads to the construction o
f the modified wave operator R(Omega(+)) for certain scattered data. W
hen initial functions belong to R(Omega(+)) which denotes the range, d
omain of Omega(+), the global existence and asymptotic behavior of sol
utions of Cauchy problem for the coupled Klein-Gordon-Schrodinger equa
tions are proved.