Instability of standing waves for nonlinear Klein-Gordon equation and related system
نویسندگان
چکیده
From the result of Ginibre and Velo ([9]) the Cauchy problem for (1) is locally wellposed in the energy space X := H1(RN)×L2(RN). Thus for any (u0, u1) ∈ X there exists a unique solution ~u := (u, ∂tu) ∈ C([0, Tmax); X) of (1) with ~u(0) = (u0, u1) such that either Tmax = ∞ (global existence) or Tmax < ∞ and limt→Tmax ‖~u(t)‖X = ∞ (finite time blowup). Moreover, the solution u(t) satisfies the conservation laws of energy and charge:
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