Exponential decay for the semilinear wave equation with localized frictional and Kelvin–Voigt dissipating mechanisms

Autor:	Victor H. Gonzalez Martinez, Marcelo M. Cavalcanti
Rok vydání:	2022
Předmět:	010101 applied mathematics Physics Kelvin voigt General Mathematics Quantum electrodynamics 010102 general mathematics 0101 mathematics Exponential decay Wave equation 01 natural sciences
Zdroj:	Asymptotic Analysis. 128:273-293
ISSN:	1875-8576 0921-7134
DOI:	10.3233/asy-211706
Popis:	In the present paper, we are concerned with the semilinear viscoelastic wave equation in an inhomogeneous medium Ω subject to two localized dampings. The first one is of the type viscoelastic and is distributed around a neighborhood ω of the boundary according to the Geometric Control Condition. The second one is a frictional damping and we consider it hurting the geometric condition of control. We show that the energy of the wave equation goes uniformly and exponentially to zero for all initial data of finite energy taken in bounded sets of finite energy phase-space.
Databáze:	OpenAIRE
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