Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Serdica Mathematical Journal, Vol. 25, No 4, (1999), 321p-340p
Abstract:
In this work we analyse the nonlinear Cauchy problem
(∂tt − ∆)u(t, x) = ( λg + O(1/(1 + t + |x|)^a) ) ) ∇t,x u(t, x), ∇t,x u(t, x) ),
whit initial data u(0, x) = e u0 (x), ut (0, x) = e u1 (x). We assume a ≥ 1,
x ∈ R^n (n ≥ 3) and g the matrix related to the Minkowski space. It can be
considerated a pertubation of the case when the quadratic term has constant
coefficient λg (see Klainerman [6])
We prove a global existence and uniqueness theorem for very regular initial
data. The proof avoids a direct application of Klainermann method (Null
condition, energy conformal method), because the result is obtained by a
combination beetwen the energy estimate (norm L^2 ) and the decay estimate
(norm L^∞ ).
Description:
∗The author was partially supported by M.U.R.S.T. Progr. Nazionale “Problemi Non Lineari...”