BulDML at Institute of Mathematics and Informatics >
IMI Periodicals >
Serdica Mathematical Journal >
1999 >
Volume 25 Number 4 >

Please use this identifier to cite or link to this item:

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...”
ISSN: 1310-6600
Appears in Collections:Volume 25 Number 4

Files in This Item:

File Description SizeFormat
sjm-vol25-num4-1999-p321-p340.pdf501.2 kBAdobe PDFView/Open


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.


Valid XHTML 1.0!   Creative Commons License