Angelo Favini's Books

Degenerate Differential Equations in Banach Spaces

By: Angelo Favini,Atsushi Yagi

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Degenerate Differential Equations in Banach Spaces

By: Angelo Favini,Atsushi Yagi

This work presents a detailed study of linear abstract degenerate differential equations, using both the semigroups generated by multivalued (linear) operators and extensions of the operational method from Da Prato and Grisvard. The authors describe the recent and original results on PDEs and algebraic-differential equations, and establishes the analyzability of the semigroup generated by some degenerate parabolic operators in spaces of continuous functions.

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Page Count

338

Publisher

CRC Press

Published Date

ISBN 10

0824716779

ISBN 13

9780824716776

Degenerate Nonlinear Diffusion Equations

By: Angelo Favini,Gabriela Marinoschi

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Degenerate Nonlinear Diffusion Equations

By: Angelo Favini,Gabriela Marinoschi

The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asymptotic behaviour, discretization schemes, coefficient identification, and to introduce relevant solving methods for each of them.

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