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Asymptotics for \(\square=m^2u+G(x,t,u,u_x,u_t)\). II: Scattering theory. (English) Zbl 0241.35015

MSC:
35G25 Initial value problems for nonlinear higher-order PDEs
35B40 Asymptotic behavior of solutions to PDEs
35P25 Scattering theory for PDEs
35C15 Integral representations of solutions to PDEs
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References:
[1] J.M. Chadam, Asymtotics for \square u = m2u + G (x, t, u, u t, ux), I. Global l Existence and De-J. M. cay, Ann. Sc. Norm. summary in Bull. Amer. Math. Soc., 76, 1032-1035, (1970). Zbl0198.44304 · Zbl 0198.44304 · doi:10.1090/S0002-9904-1970-12546-0
[2] I.E. Segal, Dispersion for Non-linear Relativistic Equations, II, Ann. Scient. Ec. Norm. Sup., ser. 4, 1, 459-497, (1968). Zbl0179.42302 MR243788 · Zbl 0179.42302 · numdam:ASENS_1968_4_1_4_459_0 · eudml:81839
[3] W.A. Strauss, Decay and Asympotics for \square u = F (u), J. Functional Anal., 2, 409-457, (1968). Zbl0182.13602 · Zbl 0182.13602 · doi:10.1016/0022-1236(68)90004-9
[4] I.E. Segal, Non-linear Semi-groups, Ann. Math., 78389-364, (1963). Zbl0204.16004 MR152908 · Zbl 0204.16004 · doi:10.2307/1970347
[5] K. Yosida, Functional Analysis, Springer, Berlin-Göttingen-Heidelberg, 1965. Zbl0126.11504 · Zbl 0126.11504
[6] N. Shenk and D. Thoe, Outgoing Solutions of (- \Delta + q - k2) u = f in an Exterior Domain, J. Math Anal. Applic, 31, 81-116, (1970). Zbl0201.13202 · Zbl 0201.13202 · doi:10.1016/0022-247X(70)90121-6
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