arXiv subjects

Isadora Maria de Jesus

Publications and source records attributed to Isadora Maria de Jesus.

4 recordsLinked to original sources

arXiv2023

Asymptotic behavior of Kawahara equation with memory effect

In this work, we are interested in a detailed qualitative analysis of the Kawahara equation, a model that has numerous physical motivations such as magneto-acoustic waves in a cold plasma and gravity waves on the surface of a heavy liquid. First, we design a feedback control law, which combines a damping component and another one of finite memory-type. Then, we are capable of proving that the problem is well-posed under a condition involving the feedback gains of the boundary control and the memory kernel. Afterwards, it is shown that the energy associated with this system exponentially decays.

math.AP↗

arXiv2023

Infinite memory effects on the stability of Biharmonic Schrödinger equation

This paper deals with the stabilization of the linear Biharmonic Schrödinger equation in an $n$-dimensional open bounded domain under Dirichlet-Neumann boundary conditions considering three infinite memory terms as damping mechanisms. We show that depending on the smoothness of initial data and the arbitrary growth at infinity of the kernel function, this class of solution goes to zero with a polynomial decay rate like $t^{-n}$ depending on assumptions about the kernel function associated with the infinite memory terms.

math.AP↗

arXiv2022

On the stability of the Kawahara equation with a distributed infinite memory

This article will deal with the stabilization problem for the higher-order dispersive system, commonly called the Kawahara equation. To do so, we introduce a damping mechanism via a distributed memory term in the equation to prove that the solutions of the Kawahara equation are exponentially stable, provided that specific assumptions on the memory kernel are fulfilled. This is possible thanks to the energy method that permits to provide a decay estimate of the system energy.

math.AP↗

arXiv2022

Massera's theorems for a higher order dispersive system

This work is devoted to present Massera-type theorems for the Kawahara system, a higher order dispersive equation, posed in a bounded domain. Precisely, thanks to some properties of the semigroup and the decays of the solutions of this equation, we are able to prove its solutions are periodic, quasi-periodic and almost periodic.

math.AP↗