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Rate of Convergence for Eigenfunctions of Aharonov-Bohm Operators with a Moving Pole Read chapter Read first chapter

2017 | OriginalPaper | Chapter

New Class of Doubly Nonlinear Evolution Equations Governed by Time-Dependent Subdifferentials

Authors : Nobuyuki Kenmochi, Ken Shirakawa, Noriaki Yamazaki

Published in: Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs

Publisher: Springer International Publishing

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Abstract

We discuss a new class of doubly nonlinear evolution equations governed by time-dependent subdifferentials in uniformly convex Banach spaces, and establish an abstract existence result of solutions. Also, we show non-uniqueness of solution, giving some examples. Moreover, we treat a quasi-variational doubly nonlinear evolution equation by applying this result extensively, and give some applications to nonlinear PDEs with gradient constraint for time-derivatives.

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previous chapter A Boundary Control Problem for the Equation and Dynamic Boundary Condition of Cahn–Hilliard Type
next chapter Boundedness of Solutions to a Degenerate Diffusion Equation
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Metadata
Title
New Class of Doubly Nonlinear Evolution Equations Governed by Time-Dependent Subdifferentials
Authors
Nobuyuki Kenmochi
Ken Shirakawa
Noriaki Yamazaki
Copyright Year
2017
Book
Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs

Print ISBN: 978-3-319-64488-2

Electronic ISBN: 978-3-319-64489-9

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-64489-9_11

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