Related papers: A nonlinear inequality
This work is devoted to improve the time decay estimates for the solution and some of its derivatives of the linear structurally damped $\sigma$-evolution equations. The Pitt inequality is the main tool provided that the initial data lies…
In this short note, we present some decay estimates for nonlinear solutions of 3d quintic, 3d cubic and 2d quintic NLS (nonlinear Schr\"odinger equations).
The article provides an overview of some advances in the mathematical understanding of the nature of the kinetic equations of quantum systems of many particles. The fundamental equations of modern mathematical physics are studied, in…
We demonstrate that in three space dimensions, the scattering behaviour of semilinear wave equations with quintic-type nonlinearities uniquely determines the nonlinearity. The nonlinearity is permitted to depend on both space and time.
We demonstrate that non-exponential decays of unstable systems can be understood as yet another example of nonextensivity encountered in many physical systems and as such can be characterized by the nonextensivity parameter q.
The paper deals with positive radial solutions to a nonlinear elliptic equation with singular and decaying potential, for which several existence and nonexistence results are known, resting upon suitable compatibility conditions between the…
A spectral decomposition method is used to obtain solutions to a class of nonlinear differential equations. We extend this approach to the analysis of the fractional form of these equations and demonstrate the method by applying it to the…
We establish conditions guaranteeing that all eventually positive increasing solutions of a half-linear delay differential equation are regularly varying and derive precise asymptotic formulae for them. The results here presented are new…
In this work, we are concerned with a nonlinear wave equation with variable exponents. A distributive delay is imposed into the damping term with variable exponents nonlinearity. Firstly, we show that the global nonexistence time can be…
In this paper, we prove pointwise decay rates for cubic and higher order nonlinear wave equations, including quasilinear wave equations, on asymptotically flat and time-dependent spacetimes. We assume that the solution to the linear…
We propose a new approach to the study of (nonlinear) growth and instability for semilinear evolution equations with compact nonlinearities. We show, in particular, that compact nonlinear perturbations of a linear evolution equation can be…
Dynamical systems with quadratic or polynomial drift exhibit complex dynamics, yet compared to nonlinear systems in general form, are often easier to analyze, simulate, control, and learn. Results going back over a century have shown that…
When employing non-linear methods to characterise complex systems, it is important to determine to what extent they are capturing genuine non-linear phenomena that could not be assessed by simpler spectral methods. Specifically, we are…
In this paper, new improvement of celebrated H\"older inequality by means of isotonic linear functionals is established. An important feature of the new inequality obtained in here is that many existing inequalities related to the H\"older…
This paper is devoted to the investigation of the nonnegative solutions and the stability and asymptotic properties of the solutions of fractional differential dynamic systems involving delayed dynamics with point delays. The obtained…
In this paper, we consider the initial value problem of a specific system of cubic nonlinear Schr\"{o}dinger equations. Our aim of this research is to specify the asymptotic profile of the solution in $L^{\infty}$ as $t \to \infty$. It is…
Nonlinear systems with model uncertainty are often described by stochastic differential equations. Some techniques from random dynamical systems are discussed. They are relevant to better understanding of solution processes of stochastic…
The main objective of the paper is to establish explicit estimates on some applicable inequalities in two variables on time scales which can be used in the study of certain qualitative properties of dynamical equations on time scales.
We develop a covariant formalism to study nonlinear perturbations of dissipative and interacting relativistic fluids. We derive nonlinear evolution equations for various covectors defined as linear combinations of the spatial gradients of…
We consider a kinetic equation describing evolution of a particle distribution function in a system with nonlinear wave-particle interactions (trappings into a resonance and nonlinear scatterings). We study properties of its solutions and…