MR3379134
Tomonari WATANABE
Tomonari WATANABE
Global Existence and Decay Estimates for Quasilinear Wave Equations with Nonuniform Dissipative Term
Funkcialaj Ekvacioj. Serio Internacia
58
2015
1--42
http://fe.math.kobe-u.ac.jp/FE/FullPapers/58-1/58_1.pdf
http://www.ams.org/mathscinet-getitem?mr=MR3379134
In this paper, we study a Cauchy problem for quasilinear wave equations with dissipative term in Sobolev space $H^L \times H^{L-1}\; (L \geq [d/2]+3)$. 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 rescaling argument. Using the argument, we obtain a global existence theorem and decay estimates with additional assumptions for the initial data.
Dissipative quasilinear wave equations, Space variable coefficients, Time decay estimates.
35L72, 35L15.
58-1
2015
Global Existence and Decay Estimates for Quasilinear Wave Equations with Nonuniform Dissipative Term
Tomonari WATANABE
Tomonari WATANABE
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