Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/454

 Title: Null Condition for Semilinear Wave Equation with Variable Coefficients Authors: Catalano, Fabio Issue Date: 1999 Publisher: 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...” URI: http://hdl.handle.net/10525/454 ISSN: 1310-6600 Appears in Collections: Volume 25 Number 4

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