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Browsing by Subject "exponential decay"

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  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    Exponential decay of solutions to a class of fourth-order nonlinear hyperbolic equations modeling the oscillations of suspension bridges
    (Wydawnictwa AGH, 2022) Liu, Yang; Yang, Chao
    This paper is concerned with a class of fourth-order nonlinear hyperbolic equations subject to free boundary conditions that can be used to describe the nonlinear dynamics of suspension bridges.
  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    Global solutions for a nonlinear Kirchhoff type equation with viscosity
    (Wydawnictwa AGH, 2023) Lapa, Eugenio Cabanillas
    In this paper we consider the existence and asymptotic behavior of solutions of the following nonlinear Kirchhoff type problem $u_{tt}- M\left(\,\displaystyle \int_{\Omega}|\nabla u|^{2}\, dx\right)\triangle u - \delta\triangle u_{t}= \mu|u|^{\rho-2}u\quad \text{in } \Omega \times ]0,\infty[,$ where $M(s)=\begin{cases}a-bs &\text{for } s \in [0,\frac{a}{b}[,\\ 0, &\text{for } s \in [\frac{a}{b}, +\infty[.\end{cases}$ If the initial energy is appropriately small, we derive the global existence theorem and its exponential decay.