On well-posedness of the nonlocal boundary value problem for parabolic difference equations
We consider the nonlocal boundary value problem for difference equations (uk−uk−1)/τ+Auk=φk, 1≤k≤N, Nτ=1, and u0=u[λ/τ]+φ, 0<λ≤1, in an arbitrary Banach space E with the strongly positive operator A. The well-posedness of this nonlocal boundary value problem for difference equations in various...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2004-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/S1026022604403033 |
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| Summary: | We consider the nonlocal boundary value problem for difference
equations (uk−uk−1)/τ+Auk=φk, 1≤k≤N, Nτ=1, and u0=u[λ/τ]+φ, 0<λ≤1, in an
arbitrary Banach space E with the strongly positive operator
A. The well-posedness of this nonlocal boundary value problem
for difference equations in various Banach spaces is studied. In
applications, the stability and coercive stability estimates in
Hölder norms for the solutions of the difference
scheme of the mixed-type boundary value problems for the
parabolic equations are obtained. Some results of numerical
experiments are given. |
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| ISSN: | 1026-0226 1607-887X |