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The space of initial data of the 3d boundary-value problem for a parabolic differential-difference equation in the one-dimensional case. (English. Russian original) Zbl 1270.35250
Math. Notes 92, No. 4, 580-584 (2012); translation from Mat. Zametki 92, No. 4, 636-640 (2012).
This paper concerns an initial-boundary value problem for a 1D parabolic differential-difference equation. A necessary and sufficient condition on the initial function is presented which implies existence of a strong solution.
MSC:
35K20 Initial-boundary value problems for second-order parabolic equations
39A99 Difference equations
47D06 One-parameter semigroups and linear evolution equations
46B70 Interpolation between normed linear spaces
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References:
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