Regularization and Approximation of Second Order Evolution Equations

Citeable URL: https://ir.library.oregonstate.edu/concern/articles/t722h9627

Descriptions

Attribute Name	Values
Creator	Showalter, R. E.
Abstract	We give a nonstandard method of integrating the equation Bu" + Cu’ + Au = f in Hilbert space by reducing it to a first order system in which the differentiated term corresponds to energy. Semigroup theory gives existence for hyperbolic and for parabolic cases. When C = εA, ε ≧ 0, this method permits the use of Faedo-Galerkin projection techniques analogous to the simple case of a single first order equation; the appropriate error estimates in the energy norm are obtained. We also indicate certain singular perturbations which can be used to approximate the equation by one which is dissipative or by one to which the above projection techniques are applicable. Examples include initial-boundary value problems for vibrations (possibly) with inertia, dynamics of rotating fluids, and viscoelasticity.
Resource Type	Article
DOI	https://doi.org/10.1137/0507037
Date Available	2014-11-05T21:16:46+00:00
Date Issued	1976-08
Citation	Showalter, R. E. (1976). Regularization and approximation of second order evolution equations. SIAM Journal on Mathematical Analysis, 7(4), 461-472. doi:10.1137/0507037
Journal Title	SIAM Journal on Mathematical Analysis
Journal Volume	7
Journal Issue/Number	4
Academic Affiliation	Mathematics
权利声明	Copyright Not Evaluated
Publisher	Society for Industrial and Applied Mathematics
Peer Reviewed	Yes
Language	English [eng]
Replaces	http://hdl.handle.net/1957/53686