Record Details

Regularization and Approximation of Second Order Evolution Equations

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Field Value
Title Regularization and Approximation of Second Order Evolution Equations
Names Showalter, R. E. (creator)
Date Issued 1976-08 (iso8601)
Note This is the publisher’s final pdf. The published article is copyrighted by the Society for Industrial and Applied Mathematics and can be found at: http://epubs.siam.org/loi/sjmaah.
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.
Genre Article
Identifier 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

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