International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 3, Pages 481-494
doi:10.1155/S0161171296000683
Time discretization of nonlinear Cauchy problems applying to mixed hyperbolic-parabolic equations
1Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, Torino 10123, Italy
2Dipartimento di Matematica, Università di Bologna Piazza di Porta San Donato 5, Bologna 40127, Italy
Received 2 March 1994; Revised 4 April 1995
Copyright © 1996 Pierluigi Colli and Angelo Favini. 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 L(d2u/dt2)+B(du/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 to
V′. 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.