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Asymptotic to systems with memory and non-local initial data

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2020
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Muñoz Rivera, Jaime E.
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Asymptotic to systems with memory and non-local initial data
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  • Muñoz Rivera, Jaime E.;
  • Poblete Oviedo, Verónica;
  • Pozo, Juan C.;
  • Vera, Octavio;
Abstract
We study the existence and the asymptotic behavior of the solution of an abstract viscoelastic system submitted to non-local initial data. u(tt )+ Au - integral(t)(0) g(t - s)Bu(s)ds = 0 u(0) = xi(u) in V, u(t) (0) = eta(u) in H, where A and B are differential operators satisfying B approximate to A(alpha) for 0 <= alpha <= 1. We prove that the model is well-posed. Concerning the asymptotic behavior, we show that the exponential decay holds if and only if alpha = 1 and g goes to zero exponentially. Otherwise if 0 <= a < 1 or the kernel goes to zero polynomially, then the solution only decays polynomially. We show the optimality of our result. Finally, we consider the non-dissipative case.
Patrocinador
Conicyt MEC Project 80150094 National Council for Scientific and Technological Development (CNPq) 310249/2018-0 PAIFAC Comision Nacional de Investigacion Cientifica y Tecnologica (CONICYT) CONICYT FONDECYT 3140103 1191137 ENL016/15
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Identifier
URI: https://repositorio.uchile.cl/handle/2250/175634
DOI: 10.1142/S0129055X20500142
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Reviews in Mathematical Physics Volumen: 32 Número: 5 Jun 2020
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