Degenerate nonlinear diffusion equations / Angelo Favini, Gabriela Marinoschi.

By: Favini, A. (Angelo), 1946-
Contributor(s): Marinoschi, Gabriela
Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag): 2049.Publisher: Berlin ; New York : Springer, ©2012Description: 1 online resource (xx, 143 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9783642282850; 3642282857; 3642282849; 9783642282843Subject(s): Burgers equation | Burgers equation | Mathematics | Differential equations, partial | Mathematical optimization | Partial Differential Equations | Calculus of Variations and Optimal Control; Optimization | Applications of MathematicsGenre/Form: Electronic books. Additional physical formats: Printed edition:: No titleDDC classification: 515/.353 LOC classification: QA377 | .F38 2012Online resources: Click here to access online
Contents:
Existence for Parabolic-Elliptic Degenerate Diffusion Problems -- Existence for Diffusion Degenerate Problems -- Existence for Nonautonomous Parabolic-Elliptic Degenerate Diffusion Equations -- Parameter Identification in a Parabolic-Elliptic Degenerate Problem.
Summary: "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"--Publisher description.
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Includes bibliographical references and index.

Existence for Parabolic-Elliptic Degenerate Diffusion Problems -- Existence for Diffusion Degenerate Problems -- Existence for Nonautonomous Parabolic-Elliptic Degenerate Diffusion Equations -- Parameter Identification in a Parabolic-Elliptic Degenerate Problem.

"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"--Publisher description.

English.

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