Growth of Solutions to System of Nonlinear Wave Equations with Degenerate Damping and Strong Sources

M. A. Rammaha and Sawanya Sakuntasathien, [{it Global existence and blow up of solutions to systems of nonlinear wave equations with degenerate damping and source terms}, Nonlinear Analysis 72(2010)2658-2683], introduced and studied the concept of existence and nonexistence of solutions in a bounded domain $Omega subset R^{n}$, $n=1,2,3$. In the present work we will prove that the solutions of system of nonlinear wave equations with degenerate damping and source terms supplemented with the initial and Dirichlet boundary conditions grows exponentially in a bounded domain $Omega subset R^{n},n>0$, provided that the initial data are large enough, with positive initial energy and the strong nonlinear functions $f_{1}$ and $f_{2}$ satisfying appropriate conditions

On the radius of spatial analyticity for the higher order nonlinear dispersive equation

summary:In this work, using bilinear estimates in Bourgain type spaces, we prove the local existence of a solution to a higher order nonlinear dispersive equation on the line for analytic initial data $u_{0}$. The analytic initial data can be extended as holomorphic functions in a strip around the $x$-axis. By Gevrey approximate conservation law, we prove the existence of the global solutions, which improve earlier results of Z. Zhang, Z. Liu, M. Sun, S. Li, (2019)

ENERGY DECAY OF SOLUTION TO PLATE EQUATION WITH MEMORY IN Rn

The viscoelastic equation with fading memory in bounded space has been deeply studied by several authors. Here, the energy decay results are established for weak-viscoelastic plate equation in IRn, which depends on the behavior of both \alpha and g. The key of the proof is to construct an appropriate Lyapunov function of the system obtained after takingthe Fourier transform

GENERAL DECAY OF SOLUTION FOR COUPLED SYSTEM OF VISCOELASTIC WAVE EQUATIONS OF KIRCHHOFF TYPE WITH DENSITY IN Rn

A system of viscoelastic wave equations of Kirchhoff type is considered. For a wider class of relaxation functions, we use spaces weighted by the density function to establish a very general decay rate of the solution

On the time decay for a thermoelastic laminated beam with microtemperature effects, nonlinear weight, and nonlinear time-varying delay

This article examines the joint impacts of microtemperature, nonlinear structural damping, along with nonlinear time-varying delay term, and time-varying coefficient on a thermoelastic laminated beam, where, the equation representing the dynamics of slip is affected by the last three mentioned terms. A general decay result was established regarding the system concerned given equal wave speeds and particular assumptions related to nonlinear terms