Regularization and Approximation of Second Order Evolution Equations Public Deposited

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  • 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.
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  • 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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  • description.provenance : Approved for entry into archive by Erin Clark(erin.clark@oregonstate.edu) on 2014-11-05T21:16:46Z (GMT) No. of bitstreams: 1 ShowalterRalphMathematicsRegularizationApproximationSecond.pdf: 1054098 bytes, checksum: 0cfdec77e0bfecad38e54cb0a9578aff (MD5)
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