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Some nonlinear inequalities and applications. (English) Zbl 1330.34034

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.

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
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