A second order fractional differential equation under effects of a super damping

Ruy Coimbra Charão; Juan Torres Espinoza; Ryo Ikehata

doi:10.3934/cpaa.2020202

Article Contents

2020, Volume 19, Issue 9: 4433-4454. Doi: 10.3934/cpaa.2020202

This issue Previous Article Ground and bound state solutions for quasilinear elliptic systems including singular nonlinearities and indefinite potentials Next Article Improved blow up criterion for the three dimensional incompressible magnetohydrodynamics system

A second order fractional differential equation under effects of a super damping

1.
Department of Mathematics, Federal University of Santa Catarina, 88040-270, Florianopolis, Brazil
2.
Department of Mathematics, Division of Educational Sciences, Graduate School of Humanities and Social Sciences, Hiroshima University, Higashi-Hiroshima 739-8524, Japan

^* Corresponding author
^* Corresponding author

Received: October 31, 2019

Revised: March 31, 2020

Published: June 2020

The first author (R.C.Charão) is partially supported by Print/CAPES process 88881.310536/ 2018-00 and the third author (R. Ikehata) was supported in part by Grant-in-Aid for Scientific Research (C) 15K04958 of JSPS

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Abstract

In this work we study asymptotic properties of global solutions for an initial value problem of a second order fractional differential equation with structural damping. The evolution equation considered includes plate equation problems. We show asymptotic profiles depending on the exponents of the Laplace operators involved in the equation and optimality of the decay rates for the associated energy and the $ L^{2} $ norm of solutions.

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Mathematics Subject Classification: Primary:35L15, 35L05;Secondary:35B40, 35B65.

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