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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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