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2002 Time-dependent nonlinear evolution equations
Chin-Yuan Lin
Differential Integral Equations 15(3): 257-270 (2002).

Abstract

Of concern is the nonlinear evolution equation \begin{align} \frac{du}{dt} & \in A(t)u,\ \ 0 < t < T \notag \\ u(0) & = u_{0} \notag \end{align} in a real Banach space $ X $, where $ A(t) : D(A(t)) \subset X \longrightarrow X $ is a time-dependent, nonlinear, multivalued operator acting on $ X $. It is shown that under certain assumptions on $ A(t) $, the equation has a strong solution. Applications to nonlinear parabolic boundary value problems with time-dependent boundary conditions are given.

Citation

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Chin-Yuan Lin. "Time-dependent nonlinear evolution equations." Differential Integral Equations 15 (3) 257 - 270, 2002.

Information

Published: 2002
First available in Project Euclid: 21 December 2012

zbMATH: 1041.34049
MathSciNet: MR1870643

Subjects:
Primary: 34G25
Secondary: 47N20

Rights: Copyright © 2002 Khayyam Publishing, Inc.

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Vol.15 • No. 3 • 2002
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