Some nonlinear inequalities and applications

TL;DR

This paper establishes sufficient conditions for the decay to zero of solutions to certain nonlinear inequalities and applies these results to analyze the long-term behavior of solutions to nonlinear evolution equations, including PDEs.

Contribution

It provides new criteria for the asymptotic decay of solutions to nonlinear inequalities and demonstrates their application to nonlinear evolution equations.

Findings

Conditions ensuring solutions tend to zero as time approaches infinity.

Application to nonlinear PDEs illustrating the decay behavior.

Enhanced understanding of long-term dynamics of nonlinear evolution equations.

Abstract

Sufficient conditions are given for the relation $\lim_{t\to\infty}y(t) = 0$ to hold, where $y(t)$ is a continuous nonnegative function on $[0,1)$ satisfying some nonlinear inequalities. The results are used for a study of large time behavior of the solutions to nonlinear evolution equations. Example of application is given for a solution to some evolution equation with a nonlinear partial differential operator.