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How to Deal with Nonlinear Terms in the Non-Dissipative Case

Volume 14, Number 1 (2012), 39 - 53

How to Deal with Nonlinear Terms in the Non-Dissipative Case

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Abstract

In this work we suggest a way to estimate some nonlinear terms appearing in the study of semilinear viscoelastic problems. So far we know how to deal with these terms only when the energy is decreasing. In this case we can estimate parts of these nonlinearities by the initial energy. We solve this issue in the general case with the help of a new differential inequality.