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2008 Smoothness of inertial manifolds for semilinear evolution equations in complex Banach spaces
Satoru Takagi
Differential Integral Equations 21(1-2): 63-80 (2008).

Abstract

We study inertial manifolds for a semilinear evolution equation $du/dt+Au=F(t,u)$ in a complex Banach space. It is known that various conditions ensure existence of inertial manifolds for the equation, however, Miklavčič gave a sharp but simple condition so as to show the existence of inertial manifolds. In this paper, we show smoothness of inertial manifolds using the sharp condition with additional assumptions on $F$, and also apply to a scalar reaction diffusion equation $u_t-u_{xx}=f(t,x,u,u_x)$ with the Dirichlet boundary conditions.

Citation

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Satoru Takagi. "Smoothness of inertial manifolds for semilinear evolution equations in complex Banach spaces." Differential Integral Equations 21 (1-2) 63 - 80, 2008.

Information

Published: 2008
First available in Project Euclid: 20 December 2012

zbMATH: 1224.35046
MathSciNet: MR2479662

Subjects:
Primary: 37L25
Secondary: 34G20, 35K20, 35K58, 35K90, 47J35

Rights: Copyright © 2008 Khayyam Publishing, Inc.

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Vol.21 • No. 1-2 • 2008
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