Fractional oscillon equations; solvability and connection with classical\n oscillon equations

2020/06/04 by Flank D. M. Bezerra, Bezerra, Flank D. M., Rodiak N. Figueroa-López +3
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2006.03192

openalex publication_date 2020/06/04 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

In this paper we are concerned with the asymptotic behavior of nonautonomous\nfractional approximations of oscillon equation u_tt-
mu(t)
Deltaν+
omega(t)u_t=f(u),
x
in
Omega,
t
in
mathbbR, subject to Dirichlet\nboundary condition on \∂ \Ω, where \Ω is a bounded smooth\ndomain in \ℝ^N, N geqslant 3, the function \ω is a\ntime-dependent damping, \μ is a time-dependent squared speed of propagation,\nand f is a nonlinear functional. Under structural assumptions on \ω and\n\μ we establish the existence of time-dependent attractor for the fractional\nmodels in the sense of Carvalho, Langa, Robinson citeCLR, and Di Plinio,\nDuane, Temam citeDDT1.\n

Related

• Nonlinear oscillations and stability domains in fractional reaction-diffusion systems
• Strichartz estimates and smooth attractors for a sub-quintic wave equation with fractional damping in bounded domains
• On the Initial Boundary Value Problem to the Time-Fractional Wave Equation with Acoustic Boundary Conditions
• Long time dynamics of a fractional dissipative model of electroconvection in bounded domains
• Attractors of Caputo fractional differential equations with triangular vector fields