Degenerate nonlinear diffusion equations

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, and coefficient identification, and to introduce relevant solving methods for each case.

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  • 1 Parameter identification in a parabolic-elliptic degenerate problem.- 2 Existence for diffusion degenerate problems.- 3 Existence for nonautonomous parabolic-elliptic degenerate diffusion Equations.- 4 Parameter identification in a parabolic-elliptic degenerate problem.

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書名 Degenerate nonlinear diffusion equations
著作者等 Favini, Angelo
Marinoschi, Gabriela
シリーズ名 Lecture notes in mathematics
出版元 Springer
刊行年月 c2012
ページ数 xxi, 143 p.
大きさ 24 cm
ISBN 9783642282843
NCID BB09320817
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言語 英語
出版国 ドイツ