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...
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| Format: | Article |
| Language: | English |
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Wiley
1996-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171296000683 |
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| _version_ | 1850168470601203712 |
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| 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 |