Energy Decay for a Dissipative Wave Equation with Compactly Supported Data

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Author(s)

    • Ono Kosuke
    • Department of Mathematical Sciences The University of Tokushima

Abstract

Consider the Cauchy problem for the dissipative wave equation : utt − Δu + u = 0, u = u(x; t) in RN × (0,∞) with u(x,0) = u0(x) and ut(x,0) = u1(x). If {u0,u1} are compactly supported data from the energy space, then there exists a domain Xm in RN such that {x ∈ RN ||x| ≥ t1/2+δ} ⊊ Xm for large t ≥ 0 and ∫ Xm (|ut| + |∇u|2) dx ≤ C(1 + t)-m with m > 0 for t ≥ 0, and moreover, if u0 + u1 = 0, then ∫ Xm |u|2 dx ≤ C(1 + t)-m for t ≥ 0.

Journal

  • Journal of mathematics, the University of Tokushima

    Journal of mathematics, the University of Tokushima (45), 41-47, 2011

    The University of Tokushima

Codes

  • NII Article ID (NAID)
    110008729453
  • NII NACSIS-CAT ID (NCID)
    AA11595324
  • Text Lang
    ENG
  • Article Type
    departmental bulletin paper
  • ISSN
    1346-7387
  • Data Source
    NII-ELS  IR 
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