Doubly nonlinear evolution equations and Bean's critical-state model for type-II superconductivity

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2005, 2005(Special): 30-39. doi: 10.3934/proc.2005.2005.30

Doubly nonlinear evolution equations and Bean's critical-state model for type-II superconductivity

1.	Department of Applied Physics, School of Science and Engineering, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan

Received September 2004 Revised April 2005 Published September 2005

Abstract
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This paper is intended as an investigation of the solvability of Cauchy problem for doubly nonlinear evolution equation of the form $dv(t)/dt + \partial \lambda^t(u(t)) \in 3 f(t)$, $v(t) \in \partial \psi(u(t))$, 0 < $t$ < $T$, where $\partial \lambda^t$ and $\partial \psi$ are subdifferential operators, and @'t depends on t explicitly. Our method of proof relies on chain rules for t-dependent subdifferentials and an appropriate boundedness condition on $\partial \lambda^t$ however, it does not require either a strong monotonicity condition or a boundedness condition on $\partial \psi$. Moreover, an initial-boundary value problem for a nonlinear parabolic equation arising from an approximation of Bean's critical-state model for type-II superconductivity is also treated as an application of our abstract theory.

Keywords: Doubly nonlinear evolution equation, reflexive Banach space, time-dependent subdifferential, Bean model..

Mathematics Subject Classification: Primary: 47J35, 34G25; Secondary: 35K5.

Citation: Goro Akagi. Doubly nonlinear evolution equations and Bean's critical-state model for type-II superconductivity. Conference Publications, 2005, 2005 (Special) : 30-39. doi: 10.3934/proc.2005.2005.30

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