Time discretization of nonlinear Cauchy problems applying to mixed hyperbolic-parabolic equationsReport as inadecuate




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International Journal of Mathematics and Mathematical Sciences - Volume 19 1996, Issue 3, Pages 481-494



Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, Torino 10123, Italy

Dipartimento di Matematica, Università di Bologna Piazza di Porta San Donato 5, Bologna 40127, Italy

Received 2 March 1994; Revised 4 April 1995

Copyright © 1996 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper we deal with the equation Ld2u-dt2+Bdu-dt+Au∋f, where L and A are linear positive selfadjoint operators in a Hilbert space H and from a Hilbert space V⊂H to its dual space V′, respectively, and B is a maximal monotone operator from V toV′. By assuming some coerciveness on L+B and A, we state the existence and uniqueness of the solution for the corresponding initial value problem. An approximation via finite differences in time is provided and convergence results along with error estimates are presented.





Author: Pierluigi Colli and Angelo Favini

Source: https://www.hindawi.com/



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