Hoang, N. S.; Ramm, A. G. Some nonlinear inequalities and applications. (English) Zbl 1330.34034 J. Abstr. Differ. Equ. Appl. 2, No. 1, 84-101 (2011). Summary: 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 \([0,\infty)\) 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. Cited in 2 Documents MSC: 34A40 Differential inequalities involving functions of a single real variable 34D20 Stability of solutions to ordinary differential equations 34G20 Nonlinear differential equations in abstract spaces 47H20 Semigroups of nonlinear operators 47F05 General theory of partial differential operators Keywords:nonlinear evolution equations; stability; dynamical systems; asymptotic stability PDFBibTeX XMLCite \textit{N. S. Hoang} and \textit{A. G. Ramm}, J. Abstr. Differ. Equ. Appl. 2, No. 1, 84--101 (2011; Zbl 1330.34034) Full Text: arXiv Link