TY - JOUR
T1 - Energy Decay for Nonlinear Wave Equations with Degenerate Dissipative Terms
AU - Nakao, Mitsuhiro
PY - 1986/1/1
Y1 - 1986/1/1
N2 - Abstract Decay rates of solutions of the initial-boundary value problem for nonlinear wave equations; utt−uxx+σ(x,ut)+β(x,u)=f(x,t)onI×R+u(x,0)=u0(x),ut(x,0)=u1(x)andu|∂I×R+=0 are derived, where I is a bounded interval in R and σ(x, v) is a function such that ∂∂vσ(x,v)≥0andσ(x,v)v≥a(x)|v|r+2 with r>-1, a(x)≥ 0 and 1/a(.)εLp(I) for some 0
AB - Abstract Decay rates of solutions of the initial-boundary value problem for nonlinear wave equations; utt−uxx+σ(x,ut)+β(x,u)=f(x,t)onI×R+u(x,0)=u0(x),ut(x,0)=u1(x)andu|∂I×R+=0 are derived, where I is a bounded interval in R and σ(x, v) is a function such that ∂∂vσ(x,v)≥0andσ(x,v)v≥a(x)|v|r+2 with r>-1, a(x)≥ 0 and 1/a(.)εLp(I) for some 0
KW - degenerate dissipative term
KW - energy decay
KW - energy method
KW - nonlinear wave equation
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U2 - 10.1016/S0168-2024(08)70147-4
DO - 10.1016/S0168-2024(08)70147-4
M3 - Article
AN - SCOPUS:77957035479
VL - 18
SP - 583
EP - 596
JO - Studies in Mathematics and its Applications
JF - Studies in Mathematics and its Applications
SN - 0168-2024
IS - C
ER -