Almost Periodicity and Almost Automorphy : for Evolution Equations and Partial Functional Differential Equations - Abdallah Afoukal - 書籍 - De Gruyter - 9783111683614 - 2025年3月3日
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Abdallah Afoukal
Almost Periodicity and Almost Automorphy : for Evolution Equations and Partial Functional Differential Equations

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When we study differential equations in Banach spaces whose coefficients are linear unbounded operators, we feel that we are working in ordinary differential equations; however, the fact that the operator coefficients are unbounded makes things quite different from what is known in the classical case. Examples or applications for such equations are naturally found in the theory of partial differential equations. More specifically, if we give importance to the time variable at the expense of the spatial variables, we obtain an “ordinary differential equation” with respect to the variable which was put in evidence.

Thus, for example, the heat or the wave equation gives rise to ordinary differential equations of this kind. Adding boundary conditions can often be translated in terms of considering solutions in some convenient functional Banach space. The theory of semigroups of operators provides an elegant approach to study this kind of systems.

Therefore, we can frequently guess or even prove theorems on differential equations in Banach spaces looking at a corresponding pattern in finite dimensional ordinary differential equations.

メディア 書籍     Paperback Book   (ソフトカバーで背表紙を接着した本)
リリース済み 2025年3月3日
ISBN13 9783111683614
出版社 De Gruyter
ページ数 466
寸法 150 × 220 × 10 mm   ·   765 g

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