| Autor: |
Sergey K. Korovin, Nikolai A. Bobylev, J. K. Kim, S. Piskarev |
| Rok vydání: |
1998 |
| Předmět: |
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| Zdroj: |
Nonlinear Analysis: Theory, Methods & Applications. 33:473-482 |
| ISSN: |
0362-546X |
| DOI: |
10.1016/s0362-546x(97)00560-9 |
| Popis: |
where operator A generates C0-semigroup exp(·A). It is well-known [1] that the C0-semigroup gives the solution of (1) by the formula v(t)= exp(tA)v0 for t≥0. We consider the semidiscrete approximation of the problem (1) in the Banach spaces En: v′ n(t)=Anvn(t); t ∈ [0;∞); vn(0)= v n; with v0 n → v0 and the operators An, which generate C0-semigroups and are consistent with the operator A. We understand consistence in the sense of general approximation scheme. This general approximation scheme can be described in the following way [2]. Let En and E be Banach spaces and {pn} be the system of linear bounded operators pn :E→En with the property: ‖pnx‖En →‖x‖E as n→∞ for any x∈E |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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