Almost Periodicity and Almost Automorphy - for Evolution Equations and Partial Functional Differential Equations

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.

Product details

• Authors: Abdallah Afoukal, Brahim Es-sebbar, Khalil Ezzinbi, Gaston Mandata N’Guérékata, Gaston Mandata N'Guérékata
• Publisher: De Gruyter
• Languages: English
• Product format: Paperback / Softback
• Released: 31.03.2025
• EAN: 9783111683614
• ISBN: 978-3-11-168361-4
• No. of pages: 456
• Dimensions: 170 mm x 25 mm x 240 mm
• Weight: 765 g
• Illustrations: 3 b/w and 9 col. ill.
• Series: De Gruyter STEM
• Subjects: Natural sciences, medicine, IT, technology > Mathematics; Differentialrechnung und -gleichungen, Differentialgleichung, Differential calculus & equations, Calculus & mathematical analysis, Applied mathematics, MAT034000 MATHEMATICS / Mathematical Analysis, MAT003000 MATHEMATICS / Applied, banach spaces, Ergodic perturbations, Banach Räume, almost automorphic functions, almost periodic differential equations