General decay rates for the wave equation with mixed-type damping mechanisms on unbounded domain with finite measure

作者：Dias Silva Flavio R; Nascimento Flavio A F; Rodrigues Jose H

来源：Zeitschrift fur Angewandte Mathematik und Physik, 2015, 66(6): 3123-3145.

DOI：10.1007/s00033-015-0547-5

• Wave equation
• Unbounded domain
• Viscoelastic damping
• Frictional damping
• Stability

This paper is concerned with the study of the uniform decay rates of the energy associated with the wave equation subject to a locally distributed viscoelastic dissipation and a nonlinear frictional damping
utt - Delta u + integral(t)(o) g(t - s)div[a(x)del u(s)]ds + b(x)f(u(t)) = 0 on Omega x]0, infinity[,
where Omega subset of Rn, n 2 unbounded open set with finite measure and unbounded smooth boundary partial derivative Omega - Gamma. Supposing that the localization functions satisfy the "competitive" assumption a(x) + b(x) >= delta > 0 for all x is an element of Omega and the relaxation function g satisfies certain nonlinear differential inequalities introduced by Lasiecka et al. (J Math Phys 54(3):031504, 2013), we extend to our considered domain the prior results of Cavalcanti and Oquendo (SIAM J Control Optim 42(4):1310-1324, 2003). In addition, while in Cavalcanti and Oquendo (2003) the authors just consider exponential and polynomial decay rate estimates, in the present article general decay rate estimates are obtained.

• 出版日期2015-12