By D Daners

ISBN-10: 0582096359

ISBN-13: 9780582096356

A part of the "Pitman study Notes in arithmetic" sequence, this article covers: linear evolution equations of parabolic kind; semilinear evolution equations of parabolic style; evolution equations and positivity; semilinear periodic evolution equations; and purposes.

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Extra resources for Abstract Evolution Equations, Periodic Problems and Applications

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13) Aiε ∈ L(X0 ) and Aiε ≤ c for a suitable constant c > 0. Then . X α = [X0 , X1 ]α holds for all α ∈ (0, 1). 3. 13) for concrete operators. For operators on Lp induced by a second order elliptic boundary value problem this has been carried out by R. Seeley [110] for C ∞ -coefficients and by J. Pr¨ uß and H. Sohr [102] for weaker regularity conditions (consult also the bibliograpy given there). Notes and references: The books on interpolation theory listed at the end of Section 4 contain also the construction and further properties of the concrete interpolation methods we have presented in this section.

This kind of situation arises for instance when dealing with initial boundary value problems where the boundary operator depends on time. For a brief description of such a generalization see the Notes and References at the end of Section 5. 3. Interpolation spaces In this section we review those concepts of interpolation theory which are necessary for our purposes. Our intention is to apply interpolation theory rather than to develop it. 38 This means that we will not dwell at length in the abstract theory, developing it as far it is convenient for our purposes.

4(b) and the definition of the continuous interpolation method. D. Examples: We shall now give a description of those interpolation spaces which arise in connection with second order elliptic operators. In the bounded domain case we shall only be concerned with the Lp -formulation and the real and complex interpolation scales. For equations on Rn we shall work in the setting of BU C(Rn ) or C0 (Rn ) and consider the continuous interpolation scale. C. Let Ω, A, B be a second order elliptic boundary value problem of class C 0 .

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Abstract Evolution Equations, Periodic Problems and Applications by D Daners

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