# On Direct Lyapunov Method in Continuum Theories

## Abstract

Let *S* _{ b } be a basic motion. We consider two aspects of the direct Lyapunov method of stability theory. The first one is related to the control of perturbations of *S* _{ b } in terms of the data (stability in mean), and the second one is related to an asymptotic decay to zero for perturbation. First, for a Lyapunov functional we take the difference between the total energy of a given flow and that of the basic flow. An algorithm for computing the norm of perturbation (in a certain space) is demonstrated by three examples. We also propose the useful technique based on the general variational formulation. The algorithm consists in the choice of a test function. Precisely, we note that different test functions can be used for the same formulation and provide us with different informations. We show how to choose the test function in three examples.

### Keywords

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