Global Existence and Decay Estimates for Quasilinear Wave Equations with Nonuniform Dissipative Term

In this paper, we study a Cauchy problem for quasilinear wave equations with dissipative term in Sobolev space H-L x HL-1 (L >= [d/2] + 3). The coefficients of the dissipative term depends on space variables and may vanish in some compact region. In order to control the derivatives of the dissipative coefficients, we introduce a resealing argument. Using the argument, we obtain a global existence theorem and decay estimates with additional assumptions for the initial data.