Time discretization of nonlinear Cauchy problems applying to mixed hyperbolic-parabolic equations

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...

Full description

Saved in:
Bibliographic Details
Main Authors: Pierluigi Colli, Angelo Favini
Format: Article
Language:English
Published: Wiley 1996-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Online Access:http://dx.doi.org/10.1155/S0161171296000683
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1850168470601203712
author Pierluigi Colli
Angelo Favini
author_facet Pierluigi Colli
Angelo Favini
author_sort Pierluigi Colli
collection DOAJ
description 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.
format Article
id doaj-art-a7b32baf261a40cebb3ba0f936b26d23
institution OA Journals
issn 0161-1712
1687-0425
language English
publishDate 1996-01-01
publisher Wiley
record_format Article
series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-a7b32baf261a40cebb3ba0f936b26d232025-08-20T02:20:57ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251996-01-0119348149410.1155/S0161171296000683Time discretization of nonlinear Cauchy problems applying to mixed hyperbolic-parabolic equationsPierluigi Colli0Angelo Favini1Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, Torino 10123, ItalyDipartimento di Matematica, Università di Bologna Piazza di Porta San Donato 5, Bologna 40127, ItalyIn 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.http://dx.doi.org/10.1155/S0161171296000683nonlinear second-order evolution equationsCauchy problem existence and uniquenesstime discretizationconvergence and error estimate.
spellingShingle Pierluigi Colli
Angelo Favini
Time discretization of nonlinear Cauchy problems applying to mixed hyperbolic-parabolic equations
International Journal of Mathematics and Mathematical Sciences
nonlinear second-order evolution equations
Cauchy problem
existence and uniqueness
time discretization
convergence and error estimate.
title Time discretization of nonlinear Cauchy problems applying to mixed hyperbolic-parabolic equations
title_full Time discretization of nonlinear Cauchy problems applying to mixed hyperbolic-parabolic equations
title_fullStr Time discretization of nonlinear Cauchy problems applying to mixed hyperbolic-parabolic equations
title_full_unstemmed Time discretization of nonlinear Cauchy problems applying to mixed hyperbolic-parabolic equations
title_short Time discretization of nonlinear Cauchy problems applying to mixed hyperbolic-parabolic equations
title_sort time discretization of nonlinear cauchy problems applying to mixed hyperbolic parabolic equations
topic nonlinear second-order evolution equations
Cauchy problem
existence and uniqueness
time discretization
convergence and error estimate.
url http://dx.doi.org/10.1155/S0161171296000683
work_keys_str_mv AT pierluigicolli timediscretizationofnonlinearcauchyproblemsapplyingtomixedhyperbolicparabolicequations
AT angelofavini timediscretizationofnonlinearcauchyproblemsapplyingtomixedhyperbolicparabolicequations