Global existence and decay estimates for quasilinear wave equations with nonuniform dissipative term

2013/11/26 by Tomonari Watanabe, Watanabe, Tomonari
Engineering · Mathematics · #35L15 #35L72 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Stability and Controllability of Differential Equations #math.AP #msc:35L15 #msc:35L72

paper · pdf · doi:10.48550/arxiv.1311.6573

42 pages

arxiv created 2013/11/26 · openalex publication_date 2013/11/26 · arxiv updated 2013/11/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We study global existence and decay estimates for quasilinear wave equations with dissipative terms in the Sobolev space H^L × H^L-1, where L ≥ [d/2]+3. The linear dissipative terms depend on space variable coefficient, and these terms may vanish in some compact region. For the proof of global existence, we need estimates of higher order energies. To control derivatives of the dissipative coefficient, we introduce an argument using the rescaling. Furthermore we get the decay estimates with additional assumptions on the initial data. To obtain the decay estimates, the rescaling argument is also needed.

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