Document Zbl 1280.47054

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Budochkina, S. A.; Savchin, V. M.

On direct variational formulations for second order evolutionary equations. (English) Zbl 1280.47054

Eurasian Math. J. 3, No. 4, 23-34 (2012).

This paper is mainly concerned with a second order evolutionary operator. The main results establish necessary and sufficient conditions that an operator be potential with respect to a certain bilinear form. The proofs follow by standard analytic tools that exploit the properties of skew-symmetric operators. The abstract results are illustrated by a class of evolution partial differential equations with potentials depending on the time.

Reviewer: Teodora-Liliana Rădulescu (Craiova)

Cited in 3 Documents

MSC:

47G40	Potential operators
70H03	Lagrange’s equations

Keywords:

potential operator; Gâteaux derivative; Euler-Lagrange equations

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